BV capacity for the Schrödinger operator with an inverse-square potential

DOI10.1007/s40840-022-01358-1OpenAlexW4286001575WikidataQ114218388 ScholiaQ114218388MaRDI QIDQ2082423

Yanyan Li

Publication date: 4 October 2022

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-022-01358-1

zbMATH Keywords

Schrödinger operatorSobolev inequalityfunctions of bounded variationfunctional capacity

Mathematics Subject Classification ID

Variational inequalities (49J40) Contents, measures, outer measures, capacities (28A12) Schrödinger operator, Schrödinger equation (35J10) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Cites Work

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• Gaussian \(\mathcal{BV}\) capacity
• The \(p\)-affine capacity
• The affine Sobolev-Zhang inequality on BV(\(\mathbb R^n)\)
• BV capacity on generalized Grushin plane
• Comparisons of relative BV-capacities and Sobolev capacity in metric spaces
• Gaussian capacity analysis
• The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces
• The sharp Sobolev and isoperimetric inequalities split twice
• BV spaces and the perimeters related to Schrödinger operators with inverse-square potentials and applications to the rank-one theorem
• Regularity and capacity for the fractional dissipative operator
• Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings
• Weakly Differentiable Functions
• Sobolev Spaces

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