List of publications by J. Elschner

  1. Über entartete gewöhnliche Differentialgleichungen. Math. Nachr. 68 (1975) 183-199.

  2. Über ein System gewöhnlicher linearer Differentialgleichungen mit mehreren singulären Stellen 1. Art. Math. Nachr. 73 (1976) 213-223.

  3. Über die normale Auflösbarkeit von entarteten singulären Integrodifferentialgleichungen. Demonstr. Mathem. 10 (1977) 815-826.

  4. Über die normale Auflösbarkeit von entarteten gewöhnlichen Differentialoperatoren in Räumen differenzierbarer Funktionen. Math. Nachr. 81 (1978) 169-193.

  5. Über singuläre Integrodifferentialgleichungen und das Poincare'sche Randwertproblem im entarteten Fall. Wiss. Zeitschrift TH Karl-Marx-Stadt 20 (1978) 531-540.

  6. Einige Bemerkungen zu einer Arbeit von Baouendi und Goulaouic. Beiträge zur Analysis 12 (1978) 185-198.

  7. Über ein lokales Cauchy-Problem mit mehrfachen Charakteristiken. Math. Nachr. 85 (1978) 185-193.

  8. Über eine Klasse entarteter singulärer Integrodifferentialgleichungen. Math. Nachr. 90 (1979) 197-211.

  9. Über selbstadjungierte singuläre gewöhnliche Differentialoperatoren und ein Problem von H. Triebel. Math. Nachr. 93 (1979) 53-65.

  10. (with M. Lorenz) Über den Operator $\sum \nolimits _{\vert\alpha\vert = \vert\beta\vert \le m} c _{\alpha \beta} x ^\alpha D^\beta$, Wiss. Zeitschrift TH Karl-Marx-Stadt 21 (1979) 529-534.

  11. On the difference method for degenerate ordinary differential equations (Russian). Differenc. uravn. 15 (1979) 828-839.

  12. (with B. Silbermann) Eine Klasse entarteter gewöhnlicher Differentialgleichungen und das Kollokationsverfahren zu ihrer Lösung. Czech. Math. J. 29 (1979) 551-563.

  13. Über entartete gewöhnliche Differentialoperatoren und eine Klasse entarteter singulärer Integrodifferentialgleichungen. Math. Nachr. 94 (1980) 117-142.

  14. Über die normale Auflösbarkeit von entarteten gewöhnlichen Differentialoperatoren auf einem unendlichen Intervall. Math. Nachr. 98 (1980) 165-181.

  15. Projektionsmethoden zur Lösung singulärer Zweipunkt-Randwertaufgaben. Beiträge zur Numer. Math. 8 (1980) 51-58.

  16. (with M. Lorenz) On the normal solvability of the operator $\Delta r^2 + \mu (\partial/\partial r)r + \lambda$, J. Diff. Eq. 36 (1980) 408-424.

  17. Über entartete Randwertprobleme für elliptische Differentialgleichungen zweiter Ordnung in der Ebene. Report R-04/80, Akad. Wiss. DDR, Inst. Math., Berlin 1980.

  18. (with B. Silbermann) Entartete gewöhnliche Differentialoperatoren und einige ihrer Verallgemeinerungen. Wiss. Schriftenreihe TH Karl-Marx-Stadt 3/1980.

  19. On degenerate boundary value problems for elliptic differential operators of second order in the plane. Math. Nachr. 102 (1981) 277-292.

  20. On a class of degenerate singular integro-differential equations. Math. Nachr. 103 (1981) 255-281.

  21. On the index of degenerate pseudodifferential operators on a closed curve. Math. Nachr. 109 (1982) 79-91.

  22. (with M. Lorenz) An unsolvable hypoelliptic differential operator degenerating at one point. Wiss. Zeitschrift TH Karl-Marx-Stadt 23 (1982) 369-373.

  23. On degenerate boundary value problems for elliptic second order differential operators in the plane. In: Differential Equations and Applications, Proceed. Second Conference, pp. 291-294, Rousse 1982.

  24. On the index of hypoelliptic one-dimensional pseudodifferential operators. In: Seminar Analysis 1981/82, Akad. Wiss. DDR, Inst. Math., pp. 11-26, Berlin 1982.

  25. (with G. Schmidt) On spline interpolation in periodic Sobolev spaces. Preprint 01/83, Akad. Wiss. DDR, Inst. Math., Berlin 1983.

  26. A Galerkin method with finite elements for degenerate one dimensional pseudodifferential equations. Math. Nachr. 111 (1983) 111-126.

  27. (with M. Lorenz) On a class of elliptic differential operators degenerating at one point. In: Banach Center Publications, vol. 10, pp. 69-78, PWN, Warsaw 1983.

  28. Galerkin methods with splines for singular integral equations over (0,1), Numer. Math. 43 (1984) 265-281.

  29. (with S. Prößdorf) Finite element methods for singular integral equations on an interval. Engineering Analysis 1 (1984) 83-87.

  30. (with S. Prößdorf, A. Rathsfeld, G. Schmidt) Spline approximation of singular integral equations. Demonstr. Mathem. 18 (1985) 661-671.

  31. ''Singular ordinary differential operators and pseudodifferential equations''. Akademie-Verlag, Berlin 1985 and Lecture Notes in Mathem. 1128, Springer, Berlin etc. 1985.

  32. On pseudodifferential operators of Mellin type. In: Seminar Analysis 1984/85, Akad. Wiss. DDR, Inst. Math., pp. 129-146, Berlin 1985.

  33. On suboptimal convergence of finite element methods for pseudodifferential equations on a closed curve. Math. Nachr. 128 (1986) 115-128.

  34. On spline collocation for singular integral equations on an interval. In: Seminar Analysis 1985/86, Akad. Wiss. DDR, Inst. Math., pp. 31-54, Berlin 1986.

  35. Asymptotics of solutions to pseudodifferential equations of Mellin type. Math. Nachr. 130 (1987) 267-305.

  36. On suboptimal convergence of finite element methods. In: Differential Equations and Applications, Proceed. Third Conference, pp. 627-630, Rousse 1987.

  37. On spline approximation for singular integral equations on an interval. Math. Nachr. 139 (1988) 309-319.

  38. On spline approximation for a class of integral equations I: Galerkin and collocation methods with piecewise polynomials. Math. Methods Appl. Sci. 10 (1988) 543-559.

  39. On spline approximation for a class of integral equations II: Galerkin's method with smooth splines. Math. Nachr. 140 (1989) 273-283.

  40. On spline approximation for a class of integral equations III: Collocation methods with piecewise linear splines. In: Seminar Analysis 1986/87, Akad. Wiss. DDR, Inst. Math., pp. 25-40, Berlin 1987.

  41. On spline approximation for convolution equations. In: Splines in numerical analysis, pp. 47-54, Akademie-Verlag, Berlin 1989.

  42. On spline collocation for convolution equations. Integral Equations and Operator Theory 12 (1989) 486-510.

  43. On spline approximation for a class of non-compact integral equations. Math. Nachr. 146 (1990) 271-321.

  44. The double layer potential operator over polyhedral domains I: Solvability in weighted Sobolev spaces. Applicable Analysis 45 (1992) 117-134.

  45. The double layer potential operator over polyhedral domains II: Spline Galerkin methods. Math. Meth. Appl. Sci. 15 (1992) 23-37.

  46. On the double layer potential over polyhedral domains. In: Symposium ''Analysis on Manifolds with Singularities'', Breitenbrunn 1990, pp. 57-64, Teubner-Texte zur Mathematik, Bd. 131, Leipzig 1992.

  47. On the exponential convergence of spline approximation methods for Wiener-Hopf equations. Math. Nachr. 160 (1993) 253-264.

  48. The h-p-version of spline approximation methods for Mellin convolution equations. J. Integral Eq. Appl. 5 (1993) 47-73.

  49. (with I.G. Graham) An optimal order collocation method for first kind boundary integral equations on polygons. Numer. Math. 70 (1995) 1-31.

  50. (with I.G. Graham) Parametrization methods for first kind integral equations on non-smooth boundaries. In: Lecture Notes in Pure and Applied Mathematics, vol. 167, pp. 81-99, Marcel Dekker, New York 1995.

  51. On the exponential convergence of some boundary element methods for Laplace's equation in non-smooth domains. In: Lecture Notes in Pure and Applied Mathematics, vol. 167, pp. 69-80, Marcel Dekker, New York 1995.

  52. (with S. Prößdorf, I.H. Sloan) The qualocation method for Symm's integral equation on a polygon. Math. Nachr. 177 (1996) 81-108.

  53. Collocation and quadrature methods for Symm's integral equation on curves with corners. Proceedings of ICIAM 95. ZAMM 76 (1996) Suppl. 1, 11-14.

  54. (with E. Stephan) A discrete collocation method for Symm's integral equation on curves with corners. J. Comput. Appl. Math. 75 (1996) 131-146.

  55. (with I.G. Graham) Quadrature methods for Symm's integral equation on polygons. IMA J. Numer. Anal. 17 (1997) 643-664.

  56. (with Y. Jeon, I.H. Sloan, E. Stephan) The collocation method for mixed boundary value problems on domains with curved polygonal boundaries. Numer. Math. 76 (1997) 355-381.

  57. (with Y. Jeon, I.H. Sloan, E. Stephan) Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary. Advances in Computational Mathematics 7 (1997) 547-571.

  58. (with H.-J. Rostalski et al) Use of a multilayer dielectric diffraction grating as the resonator mirror of a neodynium-doped yttrium aluminium garnet laser. Journal of Modern Optics 45 (1998) 1523-1535.

  59. (with G. Schmidt) Diffraction in periodic structures and optimal design of binary gratings I: Direct problems and gradient formulas. Math. Meth. Appl. Sci. 21 (1998) 1297-1342.

  60. (with G. Schmidt) Numerical solution of optimal design problems for binary gratings. J. Comput. Physics 146 (1998) 603-626.

  61. (with O. Hansen) A collocation method for the solution of the first boundary value problem of elasticity in a polygonal domain in R2. J. Integral Eq. Appl. 11 (1999) 141-196.

  62. (with O. Hansen) Ein Kollokationsverfahren zur numerischen Lösung der Lamé-Gleichung in ebenen polygonalen Gebieten. ZAMM 79 (1999) Suppl. 3, 891-892.

  63. The work of Vladimir Maz'ya on integral and pseudodifferential operators. In: The Maz'ya anniversary collection, Vol. 1, Oper. Theory, Adv. Appl. 109, pp. 35-52, Birkhäuser, Basel, 1999.

  64. (with R. Hinder, F. Penzel, G. Schmidt) Existence, uniqueness and regularity for solutions of the conical diffraction problem. Math. Models Methods Appl. Sci. 10 (2000) 317-341.

  65. (with I.G. Graham) Numerical methods for integral equations of Mellin type. J. Comput. Appl. Math. 125 (2000) 423-437.

  66. (with G. Schmidt) Diffraction in periodic structures and optimal design of binary gratings II. Gradient formulas for TM polarization. In: Siegfried Prössdorf Memorial Volume, Oper. Theory: Adv. Appl. 121, Birkhäuser, Basel, 2001, pp. 89-108.

  67. (with G. Schmidt) Inverse scattering for periodic structures: stability of polygonal interfaces. Inverse Problems 17 (2001) 1817-1829.

  68. (with R. Hinder, G. Schmidt) Finite element solution of conical diffraction problems. Advances in Computational Mathematics 16 (2002) 139-156.

  69. Inverse scattering for periodic structures: Reconstruction of grating profiles. In: Proceed. European Symposium on Numerical Methods in Electromagnetics, Toulouse, 2002, pp. 42-47.

  70. (with M. Yamamoto) An inverse problem in periodic diffractive optics: Reconstruction of Lipschitz grating profiles. Applicable Analysis 81 (2002) 1307-1328.

  71. (with R. Güther et al) Determination of longitudinal and transverse shifts of three-dimensional Gaussian beams reflected at a grating near an anomaly. Journal of Modern Optics 49 (2002) 1785-1793.

  72. (with G. Schmidt) Conical diffraction by periodic structures: Variation of interfaces and gradient formulas. Math. Nachr. 252 (2003) 24-42.

  73. (with G. Bruckner) A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles. Inverse Problems 19 (2003) 315-329.

  74. (with R. Hinder, G. Schmidt) Direct and inverse problems for diffractive structures - Optimization of binary gratings. In: Mathematics - Key Technology for the Future, Springer, Berlin, 2003, pp. 293-304.

  75. (with G. Schmidt, M. Yamamoto) An inverse problem in periodic diffractive optics: global uniqueness with a single wave number. Inverse Problems 19 (2003) 779-787.

  76. (with G. Schmidt, M. Yamamoto) Global uniqueness in determining rectangular periodic structures by scattering data with a single wave number. J. Inverse Ill-Posed Probl. 11 (2003) 235-244.

  77. (with G. Bruckner, M. Yamamoto) An optimization method for profile reconstruction. In: Progress in Analysis, Proceed. 3rd ISAAC congress, World Scientific, Singapore, 2003, pp. 1391-1404.

  78. (with G.C. Hsiao, A. Rathsfeld) Grating profile reconstruction based on finite elements and optimization techniques. SIAM J. Appl. Math. 64 (2003) 525-545.

  79. (with V. Maz'ya, J. Rehberg, G. Schmidt) Solutions for quasilinear nonsmooth evolution systems in L^p. Arch. Rational Mech. Anal. 171 (2004) 219-262.

  80. (with M. Yamamoto) Uniqueness results for an inverse periodic transmission problem. Inverse Problems 20 (2004) 1841-1852.

  81. (with G. Bruckner) The numerical solution of an inverse periodic transmission problem. Math. Meth. Appl. Sci. 28 (2005) 757-778.

  82. (with M. Yamamoto) Uniqueness in determining polygonal sound-hard obstacles with a single incoming wave. Inverse Problems 22 (2006) 355-364.

  83. (with M. Yamamoto) Uniqueness in determining polygonal periodic structures. Z. Anal. Anwendungen 26 (2007) 165-177.

  84. (with H.-C. Kaiser, J. Rehberg, G. Schmidt) W^{1,q} regularity results for elliptic transmission problems on heterogeneous polyhedra. Math. Models Methods Appl. Sci. 17 (2007) 593-615.

  85. (with J. Rehberg, G. Schmidt) Optimal regularity for elliptic transmission problems including C^1 interfaces. Interfaces and Free Boundaries 9 (2007) 233-252.

  86. (with M. Yamamoto) Uniqueness in determining polyhedral sound-hard obstacles with a single incoming wave. Inverse Problems 24 (2008) 035004 (7pp).

  87. (with G.C. Hsiao, A. Rathsfeld) An inverse problem for fluid-solid interaction. Inverse Problems and Imaging 2 (2008) 83-120.

  88. (with G.C. Hsiao, A. Rathsfeld) An optimization method in inverse acoustic scattering by an elastic obstacle. SIAM J. Appl. Math. 70 (2009) 168-187.

  89. (with M. Yamamoto) Uniqueness in inverse elastic scattering with finitely many incident waves. Inverse Problems 26 (2010) 045005 (8pp).

  90. (with G. Hu) Global uniqueness in determining polygonal periodic structures with a minimal number of incident plane waves. Inverse Problems 26 (2010) 115002 (23pp).

  91. (with S.N. Chandler-Wilde) Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces. SIAM J. Math. Anal. 42 (2010) 2554-2580.

  92. (with G. Hu) Variational approach to scattering of plane elastic waves by diffraction gratings. Math. Meth. Appl. Sci. 33 (2010) 1924-1941.

  93. (with G.C. Hsiao, A. Rathsfeld) Reconstruction of elastic obstacles from the far-field data of scattered acoustic waves. Mem. Differential Equations Math. Phys. 53 (2011) 63-97.

  94. (with G. Hu) Inverse scattering of elastic waves by periodic structures: uniqueness under the third or fourth kind boundary conditions. Meth. Appl. Anal. 18 (2011) 215-244.

  95. (with G. Hu) Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings. J. Inverse Ill-Posed Probl. 19 (2011) 717-768.

  96. (with G. Hu) Uniqueness in inverse transmission scattering problems for multilayered obstacles. Inverse Problems and Imaging 5 (2011) 793-813.

  97. (with G. Hu) Scattering of plane elastic waves by three-dimensional diffraction gratings. Math. Models Methods Appl. Sci. 22 (2012) 1150019.

  98. (with G. Hu) An optimization method in inverse elastic scattering for one-dimensional grating profiles. Commun. Comput. Phys. 12 (2012) 1434-1460.

  99. (with G. Hu) Elastic scattering by unbounded rough surfaces. SIAM J. Math. Anal. 44 (2012) 4101-4127.

  100. (with G. Hu) Direct and inverse elastic scattering problems for diffraction gratings. In: Direct and Inverse Problems in Wave Propagation and Applications, Eds. Graham et al, De Gruyter, Berlin, 2013, pp. 101-134.

  101. (with G. Hu) Elastic scattering by unbounded rough surfaces: Solvability in weighted Sobolev spaces. Appl. Anal. 94 (2015) 251-278.

  102. (with G. Hu) Corners and edges always scatter. Inverse Problems 31 (2015) 015003 (17pp).

  103. (with G. Hu, M. Yamamoto) Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type. Inverse Problems and Imaging 9 (2015) 127-141.

  104. (with G. Hu) Acoustic scattering from corners, edges and circular cones. Arch. Rational Mech. Anal. 228 (2018) 653-690.

  105. (with G. Hu) Uniqueness and factorization method for inverse elastic scattering with a single incoming wave. Inverse Problems 35 (2019) 094002 (18pp).

  106. (with G. Hu, M. Yamamoto) Single logarithmic conditional stability in determining unknown boundaries. Appl. Anal. 99 (2020) 725-746.