Regularity and geometric estimates for minima of discontinuous functionals

DOI10.4171/RMI/827zbMath1323.35219arXiv1111.2625OpenAlexW2594276400MaRDI QIDQ2340461

Eduardo V. Teixeira, Raimundo A. Leitão

Publication date: 17 April 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.2625

zbMATH Keywords

free boundary problemsdegenerate elliptic equationsdiscontinuous functionals

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) Free boundary problems for PDEs (35R35)

Related Items (10)

Sharp regularity estimates for quasi-linear elliptic dead core problems and applications ⋮ A sequential quadratic Hamiltonian method for solving parabolic optimal control problems with discontinuous cost functionals ⋮ Free boundary regularity for a degenerate problem with right hand side ⋮ Regularity of flat free boundaries for a \(p(x)\)-Laplacian problem with right hand side ⋮ 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 ⋮ Bernoulli Free Boundary Problem for the Infinity Laplacian ⋮ Free transmission problems ⋮ A free boundary problem with subcritical exponents in Orlicz spaces ⋮ Cavity problems in discontinuous media

Cites Work

• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
• Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations
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