Higher integrability for doubly nonlinear parabolic systems

Verena Bögelein (), Frank Duzaar () and Christoph Scheven ()
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Verena Bögelein: Universität Salzburg
Frank Duzaar: Universität Erlangen–Nürnberg
Christoph Scheven: Universität Duisburg-Essen

Partial Differential Equations and Applications, 2022, vol. 3, issue 6, 1-41

Abstract: Abstract In this paper we establish a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The proof is based on a new intrinsic scaling that involves both the solution and its spatial gradient. It allows to compensate for the different scaling of the system in |u| and |Du|. The result covers the range of parameters $$p>\frac{2n}{n+2}$$ p > 2 n n + 2 and $$0

Keywords: Doubly nonlinear parabolic equation; Higher integrability; Reverse Hölder inequality; 35B65; 35K40; 35K55 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00204-0

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