REGULARITY AND EXISTENCE OF SOLUTIONS TO PARABOLIC EQUATIONS WITH NONSTANDARD p(x, t), q(x, t)-GROWTH CONDITIONS

OPUSCULA MATHEMATICA（2023）

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摘要

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-infinity bounds for the weak solutions.

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关键词

existence theory, nonlinear parabolic problems, nonstandard growth, regularity theory

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