WIAS Preprint No. 2249, (2016)
On maximal parabolic regularity for non-autonomous parabolic operators
Authors
- Disser, Karoline
ORCID: 0000-0002-0222-3262 - ter Elst, A. F. M.
- Rehberg, Joachim
2010 Mathematics Subject Classification
- 35B65 47A07 35K20 35B45 46B70
Keywords
- Non-autonomous evolution equations, parabolic initial boundary value problems, maximal parabolic regularity, extrapolation of maximal parabolic regularity
DOI
Abstract
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.
Appeared in
- J. Differential Equations, 262 (2017), pp. 2039--2072.
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