Regularity of solutions of some variational inequalities

1970 ◽  
pp. 271-281 ◽  
Author(s):  
Guido Stampacchia
Keyword(s):  
Variational Inequalities ◽  
Regularity Of Solutions

scholarly journals A Note on the Regularity of the Solutions to Two Variational Inequalities Involving a Pseudodifferential Operator

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Randolph G. Cooper
Keyword(s):  
Variational Inequalities ◽  
Pseudodifferential Operator ◽  
Pseudodifferential Operators ◽  
Regularity Of Solutions ◽  
Local Operators ◽  
Regularity Results

The regularity of solutions to variational inequalities involving local operators has been studied extensively. Less attention has been paid to those involving nonlocal pseudodifferential operators. We present two regularity results for such problems.

On the regularity of solutions to quasi-linear variational inequalities of degenerate elliptic type

1977 ◽  
Vol 77 (3-4) ◽  
pp. 251-263
Author(s):  
Frances Cooper
Keyword(s):  
Variational Inequality ◽  
Sobolev Space ◽  
Variational Inequalities ◽  
Differential Inequality ◽  
Weighted Sobolev Space ◽  
Growth Conditions ◽  
Regularity Of Solutions ◽  
Elliptic Type ◽  
Degenerate Elliptic ◽  
Image Position

SynopsisUsing the theory of the weighted Sobolev space H1,2(μ), on a bounded domain Ω, in Rn, the existence and regularity of solutions u in K to the variational inequalityis established for various convex subsets K of H1, 2(μ). The growth conditions imposed on the functions A and B give the differential inequality degenerate elliptic structure, extending the results on regularity for inequalities of elliptic type.

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