The Wiener test for degenerate elliptic equations
From MaRDI portal
Publication:1166018
DOI10.5802/aif.883zbMath0488.35034OpenAlexW2042638472MaRDI QIDQ1166018
Eugene B. Fabes, Carlos E. Kenig, David S. Jerison
Publication date: 1983
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIF_1982__32_3_151_0
Related Items (98)
Finite Morse index solutions of the fractional Henon-Lane-Emden equation with Hardy potential ⋮ Hölder continuity for solutions of linear degenerate elliptic equations under minimal assumptions ⋮ Boundary regularity for a degenerate elliptic equation with mixed boundary conditions ⋮ On the multiplicity of non radial solutions for singular elliptic equations ⋮ Fractional elliptic equations, Caccioppoli estimates and regularity ⋮ Extension properties and boundary estimates for a fractional heat operator ⋮ Fractional Hardy-Hénon equations on exterior domains ⋮ Evolutionary weighted \(p\)-Laplacian with boundary degeneracy ⋮ Local properties of variational solutions for the two-obstacle problem involving square Hörmander operators ⋮ On the classification of solutions of a semilinear elliptic equation ⋮ Applications of Boundary Harnack Inequalities for p Harmonic Functions and Related Topics ⋮ Existence of solutions for the Dirichlet problem of some degenerate semilinear elliptic equations ⋮ Degenerate lake equations: classical solutions and vanishing viscosity limit ⋮ Dirichlet forms, quasiregular functions and Brownian motion ⋮ The strong maximum principle and the Harnack inequality for a class of hypoelliptic non-Hörmander operators ⋮ Hölder continuity of weak solutions of a class of linear equations with boundary degeneracy ⋮ Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ The exponential property of solutions bounded from below to degenerate equations in unbounded domains ⋮ Existence and approximation of solutions for a class of degenerate elliptic equations with Neumann boundary condition ⋮ A Saint-Venant type principle for Dirichlet forms on discontinuous media ⋮ Liouville type theorems and regularity of solutions to degenerate or singular problems. II: Odd solutions ⋮ Comportamento alla frontiera per soluzioni di equazioni ellittiche e paraboliche ⋮ Boundedness of operators related to a degenerate Schrödinger semigroup ⋮ Thin sets in weighted potential theory and degenerate elliptic equations ⋮ Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations ⋮ Sharp constants in weighted trace inequalities on Riemannian manifolds ⋮ Limits of variational problems for Dirichlet forms in varying domains ⋮ Wolff-potential estimates and doubling of subelliptic \(p\)-harmonic measures ⋮ On the dimension of \(p\)-harmonic measure in space ⋮ A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian ⋮ Boundary estimates for solutions to operators of \(p\)-Laplace type with lower order terms ⋮ Boundedness of fractional heat semigroups generated by degenerate Schrödinger operators ⋮ Pointwise weak existence for diffusions associated with degenerate elliptic forms and 2-admissible weights ⋮ Existence and almost uniqueness for \(p\)-harmonic Green functions on bounded domains in metric spaces ⋮ An invariant Harnack inequality for a class of subelliptic operators under global doubling and Poincaré assumptions, and applications ⋮ Multiple solutions for some strongly degenerate second order elliptic equations ⋮ Volume growth, capacity estimates, \(p\)-parabolicity and sharp integrability properties of \(p\)-harmonic Green functions ⋮ The regularity problem for degenerate elliptic operators in weighted spaces ⋮ Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations ⋮ Polyharmonic capacity and Wiener test of higher order ⋮ Boundary estimates and a Wiener criterion for the fractional Laplacian ⋮ Periodic solutions of fractional Laplace equations: least period, axial symmetry and limit ⋮ Lipschitz continuity of probability kernels in the optimal transport framework ⋮ Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian ⋮ On the nodal set of solutions to degenerate or singular elliptic equations with an application to \(s\)-harmonic functions ⋮ Mixed boundary value problem for \(p\)-harmonic functions in an infinite cylinder ⋮ Unnamed Item ⋮ The Wiener test for degenerate elliptic equations ⋮ Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates ⋮ Free boundary problems involving singular weights ⋮ Wiener regularity for large solutions of nonlinear equations ⋮ A class of degenerate nonlinear elliptic equations in weighted Sobolev space ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ Dahlberg's theorem in higher co-dimension ⋮ Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients ⋮ Wiener criterion for \(X\)-elliptic operators ⋮ One-dimensional symmetry for the solutions of a three-dimensional water wave problem ⋮ Wiener criterion and potential estimates for obstacle problems relative to degenerate elliptic operators ⋮ Regularity of the solutions of degenerate elliptic equations in divergent form ⋮ The boundary behavior of a solution to the Dirichlet problem for a linear degenerate second order elliptic equation ⋮ On local behavior of singular positive solutions to nonlocal elliptic equations ⋮ Weighted \(L_ p\)-potential theory on homogeneous groups ⋮ Estimates of the Green function for X-elliptic operators ⋮ An Extension Problem Related to the Fractional Laplacian ⋮ The nodal set of solutions to anomalous equations ⋮ Weighted sobolev inequalities and harmonic measure ssociated with quasiregular functions ⋮ Note on \(p\)-harmonic measure ⋮ Variational problems with free boundaries for the fractional Laplacian ⋮ Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains ⋮ Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian ⋮ Removability of the logarithmic singularity for the elliptic PDEs with measurable coefficients and its consequences ⋮ Locally \(p\)-admissible measures on \(\mathbf{R}\) ⋮ The Dirichlet problem in domains with lower dimensional boundaries ⋮ Unnamed Item ⋮ Conical square functions for degenerate elliptic operators ⋮ Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation ⋮ Green functions for weighted subelliptic \(p\)-Laplace operator constructed by Hörmander's vector fields ⋮ Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces ⋮ Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result ⋮ Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions ⋮ Interior regularity estimates for a degenerate elliptic equation with mixed boundary conditions ⋮ Harnack inequalities for fuchsian type weighted elliptic equations ⋮ The boundary Harnack principle for linear degenerate elliptic equations in Hölder domains ⋮ Harnack’s inequality for generalized subelliptic Schrödinger operators ⋮ A new elliptic measure on lower dimensional sets ⋮ Degenerate elliptic operators diagonal systems and variational integrals ⋮ Optimal Hölder Continuity for a Class of Degenerate Elliptic Problems with an Application to Subsonic-Sonic Flows ⋮ Fractional thoughts ⋮ Weighted Nonlinear Potential Theory ⋮ 𝑝 harmonic measure in simply connected domains revisited ⋮ Weighted Capacity and the Choquet Integral ⋮ Periodic solutions of non-autonomous Allen-Cahn equations involving fractional Laplacian ⋮ On the wiener type regularity of a boundary point for the polyharmonic operator ⋮ Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains ⋮ Properties of nonnegative solutions of degenerate elliptic equations ⋮ Hölder continuity of solutions of some degenerate elliptic differential equations ⋮ Elliptic Theory for Sets with Higher Co-dimensional Boundaries ⋮ Boundary estimates for solutions to linear degenerate parabolic equations
Cites Work
- The Wiener test for degenerate elliptic equations
- The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
- The local regularity of solutions of degenerate elliptic equations
- Weighted norm inequalities for maximal functions and singular integrals
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: The Wiener test for degenerate elliptic equations