Regularity of minimizers for free-discontinuity problems with p(·)-growth

DOI10.1051/cocv/2023062arXiv2303.01951OpenAlexW4386415227MaRDI QIDQ6145591

Francesco Solombrino, Chiara Leone, Giovanni Scilla, Anna Verde

Publication date: 2 February 2024

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.01951

zbMATH Keywords

regularityminimizers\(p(x)\)-growthfree-discontinuity problems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Methods involving semicontinuity and convergence; relaxation (49J45)

Cites Work

• Existence theory for a new class of variational problems
• Variable exponent functionals in image restoration
• On some variational problems
• Critical variable exponent functionals in image restoration
• Relaxation of convex functionals: the gap problem
• Existence theorem for a minimum problem with free discontinuity set
• Revisiting brittle fracture as an energy minimization problem
• Maximal regularity for local minimizers of non-autonomous functionals
• A compactness result in \(GSBV^p\) and applications to \(\varGamma \)-convergence for free discontinuity problems
• Global gradient estimates for the \(p(\cdot)\)-Laplacian
• Minimizers of the variable exponent, non-uniformly convex Dirichlet energy
• Optimal approximations by piecewise smooth functions and associated variational problems
• Hölder continuity of the gradient of p(x)-harmonic mappings
• An existence result for a nonconvex variational problem via regularity
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• VI. The phenomena of rupture and flow in solids
• Lower Semicontinuity in SBV for Integrals with Variable Growth
• On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
• Variable Exponent, Linear Growth Functionals in Image Restoration
• Regularity results for a class of functionals with non-standard growth
• Lipschitz regularity of minimizers of variational integrals with variable exponents
• Integral representation and \(\Gamma\)-convergence for free-discontinuity problems with \(p(\cdot)\)-growth
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