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

Authors : İsmail AYDIN, Cihan UNAL

Pages : 1383-1396

Doi:10.15672/hujms.561682

View : 15 | Download : 5

Publication Date : 2020-08-06

Article Type : Research Paper

Abstract :In this study, we consider weighted stochastic field exponent function spaces $L_{\vartheta }^{pinsert ignore into journalissuearticles values(.,.);}\leftinsert ignore into journalissuearticles values( D\times \Omega \right); $ and $W_{\vartheta }^{k,pinsert ignore into journalissuearticles values(.,.);}\leftinsert ignore into journalissuearticles values( 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. *********************************************************************************************************************************************************************
Keywords : Quasilinear elliptic equation, Weighted stochastic field exponent Sobolev spaces, Pseudo monotone operator, Compact embedding theorem