Nonlinear subelliptic Schrödinger type problems

DOI10.1016/S0362-546X(97)00329-5zbMath0890.35041OpenAlexW2782435224MaRDI QIDQ4374219

Marco Biroli

Publication date: 13 May 1998

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(97)00329-5

zbMATH Keywords

Harnack inequalitylocal solutionHörmander conditionsubelliptic operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Schrödinger operator, Schrödinger equation (35J10)

Cites Work

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• Balls and metrics defined by vector fields. I: Basic properties
• Fundamental solutions and geometry of the sum of squares of vector fields
• Fundamental solutions for second order subelliptic operators
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Sobolev inequalities on homogeneous spaces
• Weighted Poincaré inequalities for Hörmander vector fields and local regularity for a class of degenerate elliptic equations
• A Saint-Venant type principle for Dirichlet forms on discontinuous media
• POTENTIAL THEORY ON HOMOGENEOUS GROUPS
• Local Behavior of Solutions of Quasilinear Elliptic Equations With General Structure
• On harnack type inequalities and their application to quasilinear elliptic equations

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