P-laplace Equation In The Heisenberg Group: Regularity Of Solutions (springerbriefs In Mathematics)

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. Front Matter....Pages i-xiv Introduction....Pages 1-6 The Heisenberg Group....Pages 7-26 The p-Laplace Equation....Pages 27-42 \(C^\infty \) Regularity for the Non-degenerate Equation....Pages 43-61 Lipschitz Regularity....Pages 63-85 Back Matter....Pages 87-87