Trudinger's inequality for double phase functionals with variable exponents

Abstract

summary:Our aim in this paper is to establish Trudinger's inequality on Musielak-Orlicz-Morrey spaces $L^{\Phi ,\kappa }(G)$ under conditions on $\Phi $ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger's inequality for double phase functionals $\Phi (x,t) = t^{p(x)} + a(x) t^{q(x)}$, where $p(\cdot )$ and $q(\cdot )$ satisfy log-Hölder conditions and $a(\cdot )$ is nonnegative, bounded and Hölder continuous.

Topics & Concepts