Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations

DOI10.1016/j.jfa.2009.05.028zbMath1172.58007arXiv0905.2617OpenAlexW2092432926WikidataQ125862017 ScholiaQ125862017MaRDI QIDQ841499

Pedro J. Mendez-Hernandez, Minoru Murata

Publication date: 17 September 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.2617

zbMATH Keywords

nonnegative solutionMartin boundaryintegral representationparabolic equationelliptic equationsemismall perturbationsemi-intrinsic ultracontractivity

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Parabolic equations and parabolic systems (35K99)

Related Items

Positive solutions of Schrödinger equations in product form and Martin compactifications of the plane ⋮ On the equivalence of heat kernels of second-order parabolic operators ⋮ The Yang-Mills heat semigroup on three-manifolds with boundary ⋮ Nonnegative solutions of the heat equation on rotationally symmetric Riemannian manifolds and semismall perturbations ⋮ Widder's representation theorem for symmetric local Dirichlet spaces ⋮ A parabolic approach to Martin boundaries for elliptic equations in skew product form ⋮ Parabolic Martin boundaries and asymptotic formulas of heat kernels for one-dimensional elliptic operators with periodic coefficients ⋮ On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation ⋮ Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of Lévy processes ⋮ Ultracontractivity for Markov Semigroups and Quasi-Stationary Distributions

Cites Work

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• Martin boundary of a harmonic space with adjoint structure and its applications
• Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries
• Criticality and ground states for second-order elliptic equations
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains
• Intrinsic ultracontractivity and eigenfunction estimates for Schrödinger operators
• Lifetimes of conditioned diffusions
• Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions
• A Liouville property for Schrödinger operators
• 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
• First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains
• Heat escape
• Large time behavior of the heat kernel.
• Toward a geometric characterization of intrinsic ultracontractivity for Dirichlet Laplacians
• Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations
• Non-uniqueness of the positive Cauchy problem for parabolic equations
• Nonuniqueness of the positive Dirichlet problem for parabolic equations in cylinders
• Necessary and sufficient conditions for finiteness of lifetime
• Intrinsic ultracontractivity and small perturbation for one-dimensional generalized diffusion operators
• Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form
• Intrinsic ultracontractivity for Schrödinger operators with mixed boundary conditions
• Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains
• Representation Theorems for Positive Solutions of Parabolic Equations
• Minimal Solutions of the Heat Equation and Uniqueness of the Positive Cauchy Problem on Homogeneous Spaces
• On Strong Barriers and an Inequality of Hardy for Domains in R ⁿ
• On the behavior of the solutions of degenerate parabolic equations
• Manifolds with group actions and elliptic operators
• Uniqueness and Nonuniqueness of the Positive Cauchy Problem for the Heat Equation on Riemannian Manifolds

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