\(L_1\)-estimates for eigenfunctions and heat kernel estimates for semigroups dominated by the free heat semigroup

DOI10.1007/s00028-015-0285-3zbMath1329.35225arXiv1410.1816OpenAlexW3104793526MaRDI QIDQ904344

Hendrik Vogt

Publication date: 13 January 2016

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1816

zbMATH Keywords

Schrödinger operatorssemigroupsheat contentheat traceDirichlet LaplaciansGaussian upper boundsfree heat semigroup

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectrum, resolvent (47A10) Schrödinger operator, Schrödinger equation (35J10) Heat kernel (35K08)

Related Items (3)

Local Hardy spaces with variable exponents associated with non-negative self-adjoint operators satisfying Gaussian estimates ⋮ Solution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficients ⋮ \(L_\infty\)-estimates for the torsion function and \(L_{\infty}\)-growth of semigroups satisfying Gaussian bounds

Cites Work

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• On the Schrödinger equation and the eigenvalue problem
• Note on basic features of large time behaviour of heat kernels
• \(L_1\)-estimates for eigenfunctions of the Dirichlet Laplacian
• Sharp estimates for intrinsic ultracontractivity on \(C^{1,\alpha}\)-domains
• Heat flow out of regions in \({\mathbb{R}}^ m\)
• Dirichlet and Neumann boundary conditions: what is in between?
• Uniformly elliptic operators with measurable coefficients
• Behaviour of heat kernels of Schrödinger operators and applications to certain semilinear parabolic equations
• Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem

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