On maximal parabolic regularity for non-autonomous parabolic operators

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• 作者：Karoline Disser^a ; ^{disser@wias-berlin.de} ; A.F.M. ter Elst^b ; ^{terelst@math.auckland.ac.nz} ; Joachim Rehberg^a ; ^{rehberg@wias-berlin.de}
• 关键词：35B65 ; 47A07 ; 35K20 ; 35B45 ; 46B70
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2039-2072
• 全文大小：520 K
• 卷排序：262

文摘

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≠2r≠2. This allows us to prove maximal parabolic LrLr-regularity for discontinuous non-autonomous second-order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations.