Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential

DOI10.1080/00036811.2011.587809zbMath1255.35127OpenAlexW2032225131WikidataQ58129021 ScholiaQ58129021MaRDI QIDQ4650234

Abdelaziz Rhandi, Gisèle R. Goldstein, Jerome A. Goldstein

Publication date: 27 November 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2011.587809

zbMATH Keywords

invariant measure\(C_0\)-semigroupOrnstein-Uhlenbeck operatorspositive weak solution

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial value problems for second-order parabolic equations (35K15) Weak solutions to PDEs (35D30) Schrödinger and Feynman-Kac semigroups (47D08)

Related Items

A Zaremba-type criterion for hypoelliptic degenerate Ornstein-Uhlenbeck operators, Weighted multipolar Hardy inequalities and evolution problems with Kolmogorov operators perturbed by singular potentials, The heat equation for the Dirichlet fractional Laplacian with negative potentials: existence and blow-up of nonnegative solutions, A class of weighted Hardy inequalities and applications to evolution problems, Existence and nonexistence of positive solutions of \(p\)-Kolmogorov equations perturbed by a Hardy potential, A class of weighted Hardy type inequalities in \(\mathbb{R}^N\), A weighted Hardy inequality and nonexistence of positive solutions, The Wigner(–Poisson)–Fokker–Planck equation with singular potential, A Poincare's inequality with non-uniformly degenerating gradient, Generalized Ornstein-Uhlenbeck operators perturbed by multipolar inverse square potentials in \(L^2\)-spaces, Weighted Hardy inequalities and Ornstein-Uhlenbeck type operators perturbed by multipolar inverse square potentials, A unified approach to weighted Hardy type inequalities on Carnot groups, Weighted Hardy’s inequalities and Kolmogorov-type operators, Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation, Local and non-local improved Hardy inequalities with weights, Instantaneous blowup and singular potentials on Heisenberg groups

Cites Work

• Hardy-Littlewood theory for semigroups
• The free Markoff field
• Linear parabolic equations with strong singular potentials
• Global Properties of Transition Probabilities of Singular Diffusions
• Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier
• On the Ornstein-Uhlenbeck operator in 𝐿² spaces with respect to invariant measures
• On a degenerate heat equation with a singular potential
• Unnamed Item