p-Laplace Equation in the Heisenberg Group

Regularity of Solutions

Nonfiction, Science & Nature, Mathematics, Differential Equations
Cover of the book p-Laplace Equation in the Heisenberg Group by Diego Ricciotti, Springer International Publishing
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Author: Diego Ricciotti ISBN: 9783319237909
Publisher: Springer International Publishing Publication: December 28, 2015
Imprint: Springer Language: English
Author: Diego Ricciotti
ISBN: 9783319237909
Publisher: Springer International Publishing
Publication: December 28, 2015
Imprint: Springer
Language: English

This works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. In particular, it presents detailed proofs of smoothness for solutions to the non-degenerate equation and of Lipschitz regularity for solutions to the degenerate one. An introductory chapter presents the basic properties of the Heisenberg group, making the coverage self-contained. The setting is the first Heisenberg group, helping to keep the notation simple and allow the reader to focus on the core of the theory and techniques in the field. Further, detailed proofs make the work accessible to students at the graduate level.

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This works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. In particular, it presents detailed proofs of smoothness for solutions to the non-degenerate equation and of Lipschitz regularity for solutions to the degenerate one. An introductory chapter presents the basic properties of the Heisenberg group, making the coverage self-contained. The setting is the first Heisenberg group, helping to keep the notation simple and allow the reader to focus on the core of the theory and techniques in the field. Further, detailed proofs make the work accessible to students at the graduate level.

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