On a range of exponents for absence of Lavrentiev phenomenon for double phase functionals

DOI10.1007/s00205-022-01816-xzbMath1497.49049arXiv2110.13945OpenAlexW3210454242MaRDI QIDQ2675801

Piotr Gwiazda, Jakub Skrzeczkowski, Miroslav Bulíček

Publication date: 26 September 2022

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.13945

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) Variational methods for second-order elliptic equations (35J20) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Related Items (6)

Regularity for double phase problems at nearly linear growth ⋮ Existence and regularity results for a class of parabolic problems with double phase flux of variable growth ⋮ Gradient higher integrability for degenerate parabolic double-phase systems ⋮ Absence and presence of Lavrentiev's phenomenon for double phase functionals upon every choice of exponents ⋮ The Sobolev class where a weak solution is a local minimizer ⋮ The Lavrentiev phenomenon in calculus of variations with differential forms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounded minimisers of double phase variational integrals
• Regularity for elliptic equations with general growth conditions
• Regularity of minima: an invitation to the dark side of the calculus of variations.
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• On Lavrentiev's phenomenon
• On some variational problems
• Parametrized measures and variational principles
• Gossez's approximation theorems in Musielak-Orlicz-Sobolev spaces
• Hölder regularity for nonlocal double phase equations
• Orlicz spaces and generalized Orlicz spaces
• Regularity for general functionals with double phase
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• On the regularity of minima of non-autonomous functionals
• New examples on Lavrentiev gap using fractals
• A survey on the non-occurence of the Lavrentiev gap for convex, autonomous multiple integral scalar variational problems
• Lavrentiev gap for some classes of generalized Orlicz functions
• Parabolic equations in Musielak-Orlicz spaces with discontinuous in time \(N\)-function
• Non-occurrence of the Lavrentiev phenomenon for a class of convex nonautonomous Lagrangians
• Regularity results for generalized double phase functionals
• Regularity for double phase variational problems
• Regularity for double phase problems under additional integrability assumptions
• Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
• Harnack inequalities for double phase functionals
• Absence of Lavrentiev gap for non-autonomous functionals with \((p,q)\)-growth
• New regularity theorems for non-autonomous variational integrals with \((p,q)\)-growth
• Regularity of minimizers of \(W^{1,p}\)-quasiconvex variational integrals with \((p,q)\)-growth
• Renormalized solutions to parabolic equations in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• On the regularity of minimizers for scalar integral functionals with \((p,q)\)-growth
• Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces
• Calculus of variations

This page was built for publication: On a range of exponents for absence of Lavrentiev phenomenon for double phase functionals