Journal
ST PETERSBURG MATHEMATICAL JOURNAL
Volume 27, Issue 3, Pages 347-379Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/spmj/1392
Keywords
Functionals with nonstandard growth; Holder regularity of minimizers
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Funding
- Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)
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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.
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