Sobolev’s inequality for double phase functionals with variable exponents

By F. Maeda, Y. Mizuta, T. Ohno, Tetsu Shimomura. Forum mathematicum, 2018

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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]} .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4691933153b701a00457e6fc233cade7934b1f12

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