Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrödinger problems in uniform cones

DOI10.1007/BF02789450zbMath1146.35029OpenAlexW2047582361MaRDI QIDQ2479619

Kentaro Hirata

Publication date: 1 April 2008

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02789450

zbMATH Keywords

Schrödinger equationGreen function

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Second-order elliptic equations (35J15)

Related Items (9)

Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains ⋮ Removable singularities and singular solutions of semilinear elliptic equations ⋮ Singular solutions of nonlinear Schrödinger problem in bounded piecewise dini-smooth Jordan domain ⋮ The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations ⋮ Global estimates for non-symmetric Green type functions with applications to the \(p\)-Laplace equation ⋮ Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains ⋮ Limits at infinity of superharmonic functions and solutions of semilinear elliptic equations of Matukuma type ⋮ BOUNDARY BEHAVIOR OF SUPERHARMONIC FUNCTIONS SATISFYING NONLINEAR INEQUALITIES IN A PLANAR SMOOTH DOMAIN ⋮ Estimates of Green and Martin Kernels for Schrödinger operators with singular potential in Lipschitz domains

Cites Work

• Martin boundary points of a John domain and unions of convex sets
• Uniform domains and the quasi-hyperbolic metric
• On the existence of positive solutions of nonlinear elliptic equations -- a probabilistic potential theory approach
• Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions
• Maximum and anti-maximum principles and eigenfunctions estimates via perturbation theory of positive solutions of elliptic equations
• Semismall perturbations in the Martin theory for elliptic equations
• Singular solutions of semilinear elliptic and parabolic equations
• Estimates on the Green function and existence of positive solutions for some polyharmonic nonlinear equations in the half space
• The 3G-inequality for general Schrödinger operators on Lipschitz domains
• On positive Liouville theorems and asymptotic behavior of solutions of Fuchsian type elliptic operators
• Sharp estimates for the Green function in Lipschitz domains
• Simple counterexamples to the \(3G\)-inequality.
• Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains
• Uniform boundary Harnack principle and generalized triangle property
• The 3G inequality for a uniformly John domain
• On NTA -Conical Domains
• Conditional Gauge and Potential Theory for the Schrodinger Operator
• The lifetime of conditioned Brownian motion
• Boundary Harnack principle and Martin boundary for a uniform domain

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