Uniform Lipschitz regularity for classes of minimizers in two phase free boundary problems in Orlicz spaces with small density on the negative phase

DOI10.1016/j.anihpc.2013.07.006zbMath1301.49097OpenAlexW2005421106MaRDI QIDQ457840

J. Ederson M. Braga, Diego R. Moreira

Publication date: 29 September 2014

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2013.07.006

zbMATH Keywords

minimizersOrlicz spacesfree boundary problemsLipschitz regularitydegenerate/singular elliptic equations

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Regularity of solutions in optimal control (49N60) Free boundary problems for PDEs (35R35) Singular elliptic equations (35J75)

Related Items (14)

Nonlinear gradient estimates for generalized elliptic equations with nonstandard growth in nonsmooth domains ⋮ Global weighted Orlicz estimates for irregular obstacle problems with general growth over bounded nonsmooth domains ⋮ Domain variation solutions for degenerate two phase free boundary problems ⋮ On the full regularity of the free boundary for minima of Alt–Caffarelli functionals in Orlicz spaces ⋮ An inhomogeneous version of the Carleson estimate for singular/degenerate nonlinear equations ⋮ A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities ⋮ Stratification of free boundary points for a two-phase variational problem ⋮ A new discrete monotonicity formula with application to a two-phase free boundary problem in dimension two ⋮ Classification of nonnegative \(g\)-harmonic functions in half-spaces ⋮ On the Lipschitz regularity and asymptotic behaviour of the free boundary for classes of minima of inhomogeneous two-phase alt-caffarelli functionals in Orlicz spaces ⋮ Free boundary theory for non-homogeneous fully non-linear equations with unbounded ingredients and quadratic growth in the gradient ⋮ Inhomogeneous Hopf-Oleĭnik lemma and regularity of semiconvex supersolutions via new barriers for the Pucci extremal operators ⋮ Optimal regularity for variational solutions of free transmission problems ⋮ A free boundary problem with subcritical exponents in Orlicz spaces

Cites Work

• A two phase elliptic singular perturbation problem with a forcing term
• On the Lipschitz regularity of solutions of a minimum problem with free boundary
• A minimum problem with free boundary in Orlicz spaces
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• A minimum problem with free boundary for a degenerate quasilinear operator
• A singular energy minimizing free boundary
• Variational problems with two phases and their free boundaries
• Global energy minimizers for free boundary problems and full regularity in three dimensions
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
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