Rigidity Results for Some Boundary Quasilinear Phase Transitions

DOI10.1080/03605300902892402zbMath1188.35091arXiv0803.1382OpenAlexW2011375478MaRDI QIDQ3643213

Yannick Sire, Enrico Valdinoci

Publication date: 10 November 2009

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.1382

zbMATH Keywords

Poincaré-type inequalityquasilinear equationsAllen-Cahn phase transition

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Degenerate elliptic equations (35J70) A priori estimates in context of PDEs (35B45) Pseudodifferential operators (47G30)

Related Items

Rigidity results in diffusion Markov triples, The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation, Higher Sobolev regularity for the fractional \(p\)-Laplace equation in the superquadratic case, Local and global minimizers for a variational energy involving a fractional norm, Sub-solutions and a point-wise Hopf's lemma for fractional \(p\)-Laplacian, Stability of variational eigenvalues for the fractional \(p\)-Laplacian, Maximum principles and monotonicity of solutions for fractional \(p\)-equations in unbounded domains, On a fractional \((s,p)\)-Dirichlet-to-Neumann operator on bounded Lipschitz domains, Symmetry results for systems involving fractional Laplacian, A symmetry result for a general class of divergence form PDEs in fibered media, Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case, Trudinger-Moser type inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity, ON STABLE SOLUTIONS OF BOUNDARY REACTION-DIFFUSION EQUATIONS AND APPLICATIONS TO NONLOCAL PROBLEMS WITH NEUMANN DATA, A Hopf lemma and regularity for fractional \(p \)-Laplacians, Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions, Gevrey regularity for integro-differential operators

Cites Work

• Unnamed Item
• Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
• Connectivity of phase boundaries in strictly convex domains
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Relaxation of degenerate variational integrals
• Fibered nonlinearities for p(x)-Laplace equations
• An Extension Problem Related to the Fractional Laplacian
• Layer solutions in a half‐space for boundary reactions
• On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property