\begin{document}$ L^p $\end{document} Neumann problems in homogenization of general elliptic operators

2020 ◽  
Vol 40 (8) ◽  
pp. 5019-5045
Author(s):  
Li Wang ◽  
◽  
Qiang Xu ◽  
Shulin Zhou ◽  
Keyword(s):  
Elliptic Operators ◽  
Neumann Problems ◽  
General Elliptic

scholarly journals Properness and topological degree for general elliptic operators

2003 ◽  
Vol 2003 (3) ◽  
pp. 129-181 ◽  
Author(s):  
V. Volpert ◽  
A. Volpert
Keyword(s):  
Topological Degree ◽  
Unbounded Domains ◽  
Fredholm Property ◽  
Elliptic Operators ◽  
Linear Operators ◽  
Index Zero ◽  
Hölder Spaces ◽  
Nonlinear Operators ◽  
General Elliptic ◽  
Holder Spaces

The paper is devoted to general elliptic operators in Hölder spaces in bounded or unbounded domains. We discuss the Fredholm property of linear operators and properness of nonlinear operators. We construct a topological degree for Fredholm and proper operators of index zero.

Generalized Dirichlet and Neumann Boundary-Value Problems

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Space ◽  
Maximum Principle ◽  
Variational Inequalities ◽  
Eigenvalue Problems ◽  
Neumann Boundary ◽  
Neumann Problems ◽  
Weak Maximum Principle ◽  
General Elliptic ◽  
Neumann Boundary Value Problems ◽  
Generalized Dirichlet

In this chapter, the generalized or weak interpretation of the Dirichlet and Neumann problems for general elliptic expressions is motivated and then the Lax–Milgram Theorem is used to set the problems in the framework of eigenvalue problems for operators acting in Hilbert space. Results on variational inequalities in Chapter IV are applied to establish Stampacchia’s weak maximum principle, and this leads to the notion of capacity.

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