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The class of non-autonomous functionals under study is characterized by the fact that the energy density changes its ellipticity and growth properties according to the point; some regularity results are proved for related minimizers. These results are the borderline counterpart of analogous ones previously derived for non-autonomous functionals with (p, q)-growth. Also, similar functionals related to Musielak-Orlicz spaces are discussed, in which basic properties like the density of smooth functions, the boundedness of maximal and integral operators, and the validity of Sobolev type inequalities are naturally related to the assumptions needed to prove the regularity of minima.
Rachid Guerraoui, Jovan Komatovic, Pierre Philippe Civit, Manuel José Ribeiro Vidigueira, Seth Gilbert
Nicolas Henri Bernard Flammarion
Luis Guillermo Villanueva Torrijo, Seniz Esra Küçük, Soumya Yandrapalli, Victor Plessky