scholarly journals Solvability of the Poisson equation in weighted Sobolev spaces

2010 ◽  
Vol 37 (3) ◽  
pp. 325-339 ◽  
Author(s):  
Wojciech M. Zajączkowski
Keyword(s):  
Poisson Equation ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
The Poisson Equation

scholarly journals The Poisson equation in homogeneous Sobolev spaces

2004 ◽  
Vol 2004 (36) ◽  
pp. 1909-1921
Author(s):  
Tatiana Samrowski ◽  
Werner Varnhorn
Keyword(s):  
Sobolev Space ◽  
Poisson Equation ◽  
Sobolev Spaces ◽  
Exterior Domain ◽  
Smooth Boundary ◽  
Boundary Values ◽  
Homogeneous Sobolev Space ◽  
The Poisson Equation ◽  
Homogeneous Sobolev Spaces ◽  
External Forces

We consider Poisson's equation in ann-dimensional exterior domainG(n≥2)with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certainLq(G)-spaces there exists a solution in the homogeneous Sobolev spaceS2,q(G), containing functions being local inLq(G)and having second-order derivatives inLq(G)Concerning the uniqueness of this solution we prove that the corresponding nullspace has the dimensionn+1, independent ofq.

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

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