 |
|
|
Item Details
| Title:
|
LAYER POTENTIALS, THE HODGE LAPLACIAN AND GLOBAL BOUNDARY PROBLEMS IN NONSMOOTH RIEMANNIAN MANIFOLDS
|
| By: |
Mauris Mitrea, Michael Taylor |
| Format: |
Paperback |
| List price:
|
£54.00 |
|
We currently do not stock this item, please contact the publisher directly for
further information.
|
|
|
|
|
|
| ISBN 10: |
082182659X |
| ISBN 13: |
9780821826591 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 February, 2001 |
| Edition: |
UK ed. |
| Series: |
Memoirs of the American Mathematical Society No. 713 |
| Pages: |
120 |
| Description: |
Studies the boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds. This book discusses the theory for Cauchy type operators on Lipschitz submanifolds of co dimension one (focused on boundedness properties and jump relations). |
| Synopsis: |
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds. In the first part (ss1-4), we develop a theory for Cauchy type operators on Lipschitz submanifolds of co dimension one (focused on boundedness properties and jump relations) and solve the $L^p$-Dirichlet problem, with $p$ close to $2$, for general second-order strongly elliptic systems. The solution is represented in the form of layer potentials and optimal non tangential maximal function estimates are established.This analysis is carried out under smoothness assumptions (for the coefficients of the operator, metric tensor and the underlying domain) which are in the nature of best possible. In the second part of the monograph, ss5-13, we further specialize this discussion to the case of Hodge Laplacian $\Delta:=-d\delta-\delta d$. This time, the goal is to identify all (pairs of) natural boundary conditions of Neumann type. Owing to the structural richness of the higher degree case we are considering, the theory developed here encompasses in a unitary fashion many basic PDE's of mathematical physics.Its scope extends to also cover Maxwell's equations, dealt with separately in s14. The main tools are those of PDE's and harmonic analysis, occasionally supplemented with some basic facts from algebraic topology and differential geometry. |
| Illustrations: |
bibliography |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
|
|
|
 |
|
|
|
|
|
No Cheese, Please!
A fun picture book for children with food allergies - full of friendship and super-cute characters!Little Mo the mouse is having a birthday party.
|
My Brother Is a Superhero
Luke is massively annoyed about this, but when Zack is kidnapped by his arch-nemesis, Luke and his friends have only five days to find him and save the world...
|
|
|
|
|