First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains
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Publication:1385421
DOI10.1007/BF02843153zbMath0944.58016MaRDI QIDQ1385421
Publication date: 18 September 2000
Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)
Elliptic equations on manifolds, general theory (58J05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20)
Related Items (37)
General gauge and conditional gauge theorems ⋮ Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations ⋮ Some results and examples about the behavior of harmonic functions and Green’s functions with respect to second order elliptic operators ⋮ Positive Solutions to Schrödinger’s Equation and the Exponential Integrability of the Balayage ⋮ Unnamed Item ⋮ Dirichlet problem for the Schrödinger operator on a cone ⋮ On the equivalence of heat kernels of second-order parabolic operators ⋮ Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries ⋮ Estimates for Dirichlet heat kernels, intrinsic ultracontractivity and expected exit time on Lipschitz domains ⋮ Heat kernel and Riesz transform of Schrödinger operators ⋮ Schrödinger equations with singular potentials: linear and nonlinear boundary value problems ⋮ Green function estimates for second order elliptic operators in non-divergence form with Dini continuous coefficients ⋮ Boundary behaviors of modified Green's function with respect to the stationary Schrödinger operator and its applications ⋮ Weighted Norm Inequalities of (1, q)-Type for Integral and Fractional Maximal Operators ⋮ Dirichlet problem for the Schrödinger operator in a half space ⋮ Semilinear elliptic equations admitting similarity transformations ⋮ Criteria of solvability for multidimensional Riccati equations ⋮ Sharp two-sided heat kernel estimates of twisted tubes and applications ⋮ Anomalous slow diffusion from perpetual homogenization. ⋮ Positive solutions of a class of semilinear equations with absorption and Schrödinger equations ⋮ On the Green function and Poisson integrals of the Dunkl Laplacian ⋮ A parabolic approach to Martin boundaries for elliptic equations in skew product form ⋮ A probabilistic approach to mixed boundary value problems for elliptic operators with singular coefficients ⋮ Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains. ⋮ Retracted: Fixed point theorems for solutions of the stationary Schrödinger equation on cones ⋮ Time-reversal and elliptic boundary value problems ⋮ Global Green’s Function Estimates ⋮ Positive super-solutions to semi-linear second-order non-divergence type elliptic equations in exterior domains ⋮ Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains ⋮ Boundary Harnack Principle and the Quasihyperbolic Boundary Condition ⋮ Intrinsic ultracontractivity of a Schrödinger semigroup in \(\mathbb R^N\) ⋮ Estimates of Green and Martin Kernels for Schrödinger operators with singular potential in Lipschitz domains ⋮ Sur la convergence radiale des potentiels associés à l'équation de Helmholtz ⋮ Certain Liouville properties of eigenfunctions of elliptic operators ⋮ Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains ⋮ Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations ⋮ Integral representation for the solution of the stationary Schrödinger equation in a cone
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