Variational and Perron-Wiener solutions in stratified Lie groups

DOI10.1002/mana.201400168zbMath1339.31002OpenAlexW1829138717WikidataQ115405895 ScholiaQ115405895MaRDI QIDQ2808125

Beatrice Abbondanza

Publication date: 26 May 2016

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201400168

zbMATH Keywords

sub-LaplacianDirichlet's problemCarnot groups

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Cites Work

• Unnamed Item
• Varying domains: Stability of the Dirichlet and the Poisson problem
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Maximum Principle, Nonhomogeneous Harnack Inequality, and Liouville Theorems forX-Elliptic Operators
• On Dirichlet's principle and Poincaré's méthode de balayage
• The Dirichlet problem by variational methods
• Equivalence of weak Dirichlet's principle, the method of weak solutions and Perron's method towards classical solutions of Dirichlet's problem for harmonic functions

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