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

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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