No abstract

No abstract

Our aim in this paper is to establish generalizations of Sobolev’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 of order {\theta\in(0,1]}.

No abstract

Morrey spaces have become a good tool for the study of existence and regularity of solutions of partial differential equations. Our aim in this paper is to give Sobolev's inequality for Riesz potentials of functions in Morrey spaces.