Sobolev’s inequality for double phase functionals with variable exponents

摘要

Our aim in this paper is to establish generalizations of Sobolev’s inequalityfor double phase functionals Φ ? ( x , t ) = t p ? ( x ) + a ? ( x ) ? t q ? ( x ) {Phi(x,t)=t^{p(x)}+a(x)t^{q(x)}}