Evolution variational inequalities with growth conditions in metric spaces

2019 ◽  
Vol 248 (2) ◽  
pp. 147-169
Author(s):  
Naoki Tanaka
Keyword(s):  
Variational Inequalities ◽  
Metric Spaces ◽  
Growth Conditions ◽  
Evolution Variational Inequalities

scholarly journals Variational inequalities for energy functionals with nonstandard growth conditions

1998 ◽  
Vol 3 (1-2) ◽  
pp. 41-64 ◽  
Author(s):  
Martin Fuchs ◽  
Li Gongbao
Keyword(s):  
Variational Inequalities ◽  
Obstacle Problem ◽  
Partial Regularity ◽  
Growth Conditions ◽  
Energy Functionals ◽  
Nonstandard Growth ◽  
Bounded Lipschitz Domain ◽  
Growth Properties ◽  
Nonstandard Growth Conditions ◽  
Special Case

We consider the obstacle problem{minimize????????I(u)=?OG(?u)dx??among functions??u:O?Rsuch?that???????u|?O=0??and??u=F??a.e.for a given functionF?C2(O¯),F|?O<0and a bounded Lipschitz domainOinRn. The growth properties of the convex integrandGare described in terms of aN-functionA:[0,8)?[0,8)withlimt?8¯A(t)t-2<8. Ifn=3, we prove, under certain assumptions onG,C1,8-partial regularity for the solution to the above obstacle problem. For the special case whereA(t)=tln(1+t)we obtainC1,a-partial regularity whenn=4. One of the main features of the paper is that we do not require any power growth ofG.

scholarly journals Minimax theorems in probabilistic metric spaces

1995 ◽  
Vol 51 (1) ◽  
pp. 103-119 ◽  
Author(s):  
Y.J. Cho ◽  
S.S. Chang ◽  
J.S. Jung ◽  
S.M. Kang ◽  
X. Wu
Keyword(s):  
Variational Inequalities ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Minimax Theorems ◽  
Saddle Point Problems ◽  
Coincidence Points ◽  
Probabilistic Metric Spaces ◽  
Upper Semicontinuous Functions ◽  
Probabilistic Metric ◽  
Semicontinuous Functions

In this paper, new minimax theorems for mixed lower-upper semicontinuous functions in probabilistic metric spaces are given. As applications, we utilise these results to show the existence of solutions of abstract variational inequalities, implicit variational inequalities and saddle point problems, and the existence of coincidence points in probabilistic metric spaces.

scholarly journals Conical differentiability for evolution variational inequalities

2003 ◽  
Vol 193 (1) ◽  
pp. 131-146 ◽  
Author(s):  
Jiřı́ Jarušek ◽  
Miroslav Krbec ◽  
Murali Rao ◽  
Jan Sokołowski
Keyword(s):  
Variational Inequalities ◽  
Evolution Variational Inequalities
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