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July/August 2019 Global $L^r$-estimates and regularizing effect for solutions to the $p(t,x)$-Laplacian systems
F. Crispo, P. Maremonti, M. Růžička
Adv. Differential Equations 24(7/8): 407-434 (July/August 2019). DOI: 10.57262/ade/1556762454

Abstract

We consider the initial boundary value problem for the $p(t,x)$-Laplacian system in a bounded domain $\Omega$. If the initial data belongs to $L^{r_0}$, $r_0\geq 2$, we prove a global $L^{r_0}(\Omega)$-regularity result uniformly in $t>0$ that, in the particular case ${r_0}=\infty$, gives a maximum modulus theorem. Under the assumption $p_-=\inf p(t,x)>\frac{2n} {n+r_0}$, we also study $L^{r_0}-L^{r}$ estimates for the solution, for $r\geq r_0$.

Citation

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F. Crispo. P. Maremonti. M. Růžička. "Global $L^r$-estimates and regularizing effect for solutions to the $p(t,x)$-Laplacian systems." Adv. Differential Equations 24 (7/8) 407 - 434, July/August 2019. https://doi.org/10.57262/ade/1556762454

Information

Published: July/August 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07197892
MathSciNet: MR3945767
Digital Object Identifier: 10.57262/ade/1556762454

Subjects:
Primary: 35B65 , 35K61 , 46E35

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.24 • No. 7/8 • July/August 2019
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