Opuscula Mathematica
Opuscula Math. 43, no. 6 (2023), 759-788

Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions

Hamid El Bahja
Abstract. We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard \(p(x,t),q(x,t)\)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time \(L^{\infty}\) bounds for the weak solutions.
Keywords: existence theory, nonlinear parabolic problems, nonstandard growth, regularity theory.
Mathematics Subject Classification: 35K55, 35K65.
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About the authors ▼
Hamid El Bahja
https://orcid.org/0000-0002-0945-2105
African Institute for Mathematical Sciences, Cape Town, South Africa
About the article ▼
Communicated by J.I. Díaz.
Received: 2023-05-20.
Accepted: 2023-06-16.
Published online: 2023-07-22.
Cite this article as ▼
Hamid El Bahja, Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions, Opuscula Math. 43, no. 6 (2023), 759-788, https://doi.org/10.7494/OpMath.2023.43.6.759.
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