Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth

Year 2020, Volume: 49 Issue: 4, 1383 - 1396, 06.08.2020

İsmail Aydın , Cihan Unal

https://doi.org/10.15672/hujms.561682

Cited By: 6

Abstract

In this study, we consider weighted stochastic field exponent function spaces $L_{\vartheta }^{p(.,.)}\left( D\times \Omega \right) $ and $W_{\vartheta }^{k,p(.,.)}\left( D\times \Omega \right) $. Also, we study some basic properties and embeddings of these spaces. Finally, we present an application for defined spaces to the stochastic partial differential equations with stochastic field growth.

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Keywords

Quasilinear elliptic equation, Weighted stochastic field exponent Sobolev spaces, Pseudo-monotone operator, Compact embedding theorem

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