Layer Potentials the Hodge Laplacian and Global Boundary Problems in Nonsmooth Riemannian Manifolds is popular PDF and ePub book, written by Dorina Mitrea in 2001, it is a fantastic choice for those who relish reading online the Boundary value problems genre. Let's immerse ourselves in this engaging Boundary value problems book by exploring the summary and details provided below. Remember, Layer Potentials the Hodge Laplacian and Global Boundary Problems in Nonsmooth Riemannian Manifolds can be Read Online from any device for your convenience.
Layer Potentials the Hodge Laplacian and Global Boundary Problems in Nonsmooth Riemannian Manifolds Book PDF Summary
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 $Lp$-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.
Detail Book of Layer Potentials the Hodge Laplacian and Global Boundary Problems in Nonsmooth Riemannian Manifolds PDF
- Author : Dorina Mitrea
- Release : 26 June 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821826591
- Genre : Boundary value problems
- Total Page : 137 pages
- Language : English
- PDF File Size : 9,8 Mb
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