P Laplace Equation In The Heisenberg Group
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| Author | : Diego Ricciotti |
| Publisher | : Springer |
| Total Pages | : 96 |
| Release | : 2015-12-28 |
| Genre | : Mathematics |
| ISBN | : 331923790X |
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.
| Author | : Kristen Snyder Childers |
| Publisher | : |
| Total Pages | : |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
In [2], Beals, Gaveau and Greiner find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This fundamental solution is based on the well-known fundamental solution to the p-Laplace equation in Grushin-type spaces [4] and the Heisenberg group [6]. In this thesis, we look to generalize the work in [2] for a p-Laplace-type equation. After discovering that the "natural" generalization fails, we find two generalizations whose solutions are based on the fundamental solution to the p-Laplace equation.
| Author | : Robert D. Freeman |
| Publisher | : |
| Total Pages | : 83 |
| Release | : 2020 |
| Genre | : Geometry, Riemannian |
| ISBN | : |
In this thesis, we examine the p(x)-Laplace equation in the context of Carnot groups. The p(x)-Laplace equation is the prototype equation for a class of nonlinear elliptic partial differential equations having so-called nonstandard growth conditions. An important and useful tool in studying these types of equations is viscosity theory. We prove a p()-Poincar ́e-type inequality and use it to prove the equivalence of potential theoretic weak solutions and viscosity solutions to the p(x)-Laplace equation. We exploit this equivalence to prove a Rad ́o-type removability result for solutions to the p-Laplace equation in the Heisenberg group. Then we extend this result to the p(x)-Laplace equation in the Heisenberg group.
| Author | : Brian Street |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 768 |
| Release | : 2023-07-03 |
| Genre | : Mathematics |
| ISBN | : 3111085643 |
Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.
| Author | : Detlef Muller |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 104 |
| Release | : 2014-12-20 |
| Genre | : Mathematics |
| ISBN | : 1470409399 |
The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1
| Author | : |
| Publisher | : |
| Total Pages | : 572 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Peter Lindqvist |
| Publisher | : Springer |
| Total Pages | : 104 |
| Release | : 2019-04-26 |
| Genre | : Mathematics |
| ISBN | : 3030145018 |
This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various new topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p2). Thus it requires advanced methods. Many fascinating properties of the Laplace equation are, in some modified version, extended to the p-Laplace equation. Nowadays the theory is almost complete, although some challenging problems remain open./pbrp
| Author | : Stéphane Menozzi |
| Publisher | : Springer Nature |
| Total Pages | : 354 |
| Release | : |
| Genre | : |
| ISBN | : 9819702259 |
| Author | : |
| Publisher | : |
| Total Pages | : 804 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : David R. Adams |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 372 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3662032821 |
"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
