Abstract
Abstract Our aim in this paper is to establish generalizations of Sobolev’s inequality for 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)}} , where p ( ⋅ ) {p(\,{\cdot}\,)} and q ( ⋅ ) {q(\,{\cdot}\,)} satisfy log-Hölder conditions and a ( ⋅ ) {a(\,{\cdot}\,)} is nonnegative, bounded and Hölder continuous of order θ ∈ ( 0 , 1 ] {\theta\in(0,1]} .
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