A metric potential capacity: some qualitative properties of Schrödinger's equations with a non negative potential

DOI10.1007/s13398-022-01254-0zbMath1491.35234OpenAlexW4281254774MaRDI QIDQ2670716

Jean Michel Rakotoson

Publication date: 1 June 2022

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-022-01254-0

zbMATH Keywords

capacitySchrödinger equationvery singular potential

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Singular elliptic equations (35J75)

Cites Work

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• In between the inequalities of Sobolev and Hardy
• Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
• Semilinear elliptic equations and systems with diffuse measures
• The principle of linearized stability of a class of degenerate diffusion equations
• Linear diffusion with singular absorption potential and/or unbounded convective flow: the weighted space approach
• On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via singular potentials: the multi-dimensional case
• New Hardy inequalities and behaviour of linear elliptic equations
• Kato's inequality when \(\Delta u\) is a measure
• Nonlinear problems related to the Thomas-Fermi equation
• Blow up for \(u_ t- \Delta u=g(u)\) revisited
• Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
• A note on the dimensions of Assouad and Aikawa
• On the differentiability of very weak solutions with right-hand side data integrable with respect to the distance to the boundary
• Schrödinger operators with singular potentials
• Plongements lipschitziens dans ${\bbfR}\sp n$
• Quasiadditivity of Riesz capacity.
• Weakly Differentiable Functions
• Existence and uniqueness of solutions of Schrödinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications
• Potential-capacity and some applications
• A Theory of Capacities for Potentials of Functions in Lebesgue Classes.

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