Estimates for Dirichlet heat kernels, intrinsic ultracontractivity and expected exit time on Lipschitz domains

zbMath1277.31014MaRDI QIDQ380632

Lotfi Riahi

Publication date: 14 November 2013

Published in: Communications in Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.cma/1374153498

zbMATH Keywords

Dirichlet boundary conditionsheat kernelbounded Lipschitz domainsecond order elliptic operator

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Heat equation (35K05) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items

Fractional elliptic equations, Caccioppoli estimates and regularity ⋮ Moment bounds for some fractional stochastic heat equations on the ball ⋮ Moment bounds of a class of stochastic heat equations driven by space-time colored noise in bounded domains ⋮ Regularity estimates for nonlocal space-time master equations in bounded domains ⋮ Some effects of the noise intensity upon non-linear stochastic heat equations on \([0, 1\)]

Cites Work

• A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations
• Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts
• Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures
• Sharp estimates for intrinsic ultracontractivity on \(C^{1,\alpha}\)-domains
• Exit time, Green function and semilinear elliptic equations
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Conditional transformation of drift formula and potential theory for \(\Delta +b(\cdot)\cdot \nabla\)
• The equivalence of certain heat kernel and Green function bounds
• Intrinsic ultracontractivity and eigenfunction estimates for Schrödinger operators
• Estimates of harmonic measure
• Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions
• Intrinsic ultracontractivity of Dirichlet Laplacians in non-smooth domains
• First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains
• Pointwise properties of eigenfunctions and heat kernels of Dirichlet-Schrödinger operators
• Inequalities for Green functions in a Dini-Jordan domain in \(\mathbb{R}^2\)
• The boundary behavior of heat kernels of Dirichlet Laplacians
• The 3G-inequality for general Schrödinger operators on Lipschitz domains
• Comparison of Green functions and harmonic measures for parabolic operators
• The global behavior of heat kernels in exterior domains
• Uniform boundary Harnack principle and generalized triangle property
• Equivalence of the Green's Functions for Diffusion Operators in R n : A Counterexample
• On Strong Barriers and an Inequality of Hardy for Domains in R ⁿ
• The Integrability of Superharmonic Functions on Lipschitz Domains
• Conditional Gauge and Potential Theory for the Schrodinger Operator
• Integrability of Superharmonic Functions and Subharmonic Functions
• Gaussian Estimates in Lipschitz Domains
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item