WIAS Preprint No. 2249, (2016)
On maximal parabolic regularity for non-autonomous parabolic operators
- Disser, Karoline
- ter Elst, A. F. M.
- Rehberg, Joachim
2010 Mathematics Subject Classification
- 35B65 47A07 35K20 35B45 46B70
- Non-autonomous evolution equations, parabolic initial boundary value problems, maximal parabolic regularity, extrapolation of maximal parabolic regularity
We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r ≠ 2. This allows us to prove maximal parabolic Lr-regularity for discontinuous non-autonomous second-order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations.
- J. Differential Equations, 262 (2017), pp. 2039--2072.