On the nodal set of solutions to degenerate or singular elliptic equations with an application to \(s\)-harmonic functions

DOI10.1016/j.matpur.2020.01.010zbMath1471.35151arXiv1808.01851OpenAlexW3003827081MaRDI QIDQ2204945

Giorgio Tortone, Yannick Sire, Susanna Terracini

Publication date: 16 October 2020

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.01851

zbMATH Keywords

nodal setnonlocal diffusionmonotonicity formulasdegenerate or singular elliptic equationsblow-up classification

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Singular elliptic equations (35J75) Fractional partial differential equations (35R11)

Related Items (13)

Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations ⋮ Segregated configurations involving the square root of the Laplacian and their free boundaries ⋮ On a weighted two-phase boundary obstacle problem ⋮ Existence and uniqueness of solution for a singular elliptic differential equation ⋮ On the nodal set of solutions to degenerate or singular elliptic equations with an application to \(s\)-harmonic functions ⋮ Regularity of shape optimizers for some spectral fractional problems ⋮ Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation ⋮ Regularity results for segregated configurations involving fractional Laplacian ⋮ The nodal set of solutions to anomalous equations ⋮ Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions ⋮ An epiperimetric inequality approach to the parabolic Signorini problem ⋮ Unique continuation principles for a higher order fractional Laplace equation ⋮ The nodal set of solutions to some nonlocal sublinear problems

Cites Work

• Unnamed Item
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• On the uniqueness of solutions of a nonlocal elliptic system
• Ratios of harmonic functions with the same zero set
• Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian
• Nodal sets for solutions of elliptic equations
• Fractional Laplacian in conformal geometry
• Regularity of the nodal set of segregated critical configurations under a weak reflection law
• A unique continuation theorem for exterior differential forms on Riemannian manifolds
• Nodal sets of eigenfunctions on Riemannian manifolds
• The Wiener test for degenerate elliptic equations
• Scattering matrix in conformal geometry
• On the number of singularities for the obstacle problem in two dimensions
• On \(s\)-harmonic functions on cones
• Unique continuation for fractional orders of elliptic equations
• Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure
• Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture
• On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition
• Zero sets of solutions to semilinear elliptic systems of first order
• Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients
• Symmetric stable processes in cones
• On the nodal set of solutions to degenerate or singular elliptic equations with an application to \(s\)-harmonic functions
• Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian
• Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem
• Uniform Hölder regularity with small exponent in competition-fractional diffusion systems
• Nodal sets of harmonic functions
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• Asymptotic estimates for the spatial segregation of competitive systems
• On quantitative unique continuation properties of fractional Schrödinger equations: Doubling, vanishing order and nodal domain estimates
• Extension Problem and Harnack's Inequality for Some Fractional Operators
• Nodal sets of solutions of elliptic and parabolic equations
• Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition
• Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
• Unique continuation for elliptic operators: A geometric-variational approach
• The local regularity of solutions of degenerate elliptic equations
• Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
• Geometric measure of singular sets of elliptic equations
• Characterization of traces of the weighted Sobolev space $W^{1,p}(\Omega,d_M^\epsilon)$ on $M$
• Strong Unique Continuation Properties of Generalized Baouendi–Grushin Operators
• Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
• An Extension Problem Related to the Fractional Laplacian
• Critical Sets of Elliptic Equations

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