DUAL VARIATIONAL INEQUALITIES FOR EXTREMAL EIGENVALUE PROBLEMS

1978 ◽  
pp. 35-44
Author(s):  
Earl R. Barnes
Keyword(s):  
Variational Inequalities ◽  
Eigenvalue Problems

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.

Sign in / Sign up

Export Citation Format

Share Document