Trudinger's inequality for double phase functionals with variable exponents

DOI10.21136/CMJ.2021.0506-19OpenAlexW3122254846MaRDI QIDQ4994521

Yoshihiro Mizuta, Takao Ohno, Fumi-Yuki Maeda, Tetsu Shimomura

Publication date: 18 June 2021

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/cmj.2021.0506-19

zbMATH Keywords

Riesz potentialTrudinger's inequalityMusielak-Orlicz-Morrey spacedouble phase functional

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Potentials and capacities on other spaces (31C15)

Related Items (10)

Trudinger's inequality on Musielak-Orlicz-Morrey spaces over non-doubling metric measure spaces ⋮ Sobolev's inequality in Musielak–Orlicz–Morrey spaces of an integral form ⋮ Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces ⋮ Regularity theory for non-autonomous problems with a priori assumptions ⋮ Integrability for Hardy operators of double phase ⋮ Boundedness of integral operators of double phase ⋮ Sobolev's inequality for Musielak-Orlicz-Sobolev functions ⋮ Unnamed Item ⋮ A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces ⋮ Continuity of generalized Riesz potentials for double phase functionals with variable exponents

Cites Work

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• Bounded minimisers of double phase variational integrals
• Orlicz spaces and modular spaces
• Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent
• The maximal operator on generalized Orlicz spaces
• Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent
• Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent
• Gossez's approximation theorems in Musielak-Orlicz-Sobolev spaces
• Regularity for general functionals with double phase
• Trudinger's inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces
• Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces
• Regularity for double phase variational problems
• Sobolev's inequality for double phase functionals with variable exponents
• Trudinger's inequality for Riesz potentials of functions in Musielak-Orlicz spaces
• Non-autonomous functionals, borderline cases and related function classes
• Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents
• Continuity properties of Riesz potentials for functions in L^p(⋅) of variable exponent
• Differentiability and Holder continuity of Riesz potentials of Orlicz functions

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