Self-improving property of degenerate parabolic equations of porous medium-type
| Autor: | Sebastian Schwarzacher, Ugo Gianazza |
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| Rok vydání: | 2019 |
| Předmět: |
Lemma (mathematics)
Property (philosophy) General Mathematics 010102 general mathematics Mathematical analysis Degenerate energy levels Mathematics::Classical Analysis and ODEs Type (model theory) 01 natural sciences Parabolic partial differential equation Power (physics) Mathematics - Analysis of PDEs FOS: Mathematics 35K65 35B65 0101 mathematics Porous medium Reverse holder inequality Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | American Journal of Mathematics. 141:399-446 |
| ISSN: | 1080-6377 |
| DOI: | 10.1353/ajm.2019.0009 |
| Popis: | We show that the gradient of solutions to degenerate parabolic equations of porous medium-type satisfies a reverse H\"older inequality in suitable intrinsic cylinders. We modify the by-now classical Gehring lemma by introducing an intrinsic Calder\'on-Zygmund covering argument, and we are able to prove local higher integrability of the gradient of a proper power of the solution $u$. Comment: With respect to the previous version, a detailed application of a proper Vitali covering is given here |
| Databáze: | OpenAIRE |
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