Some Existence and Regularity Results for Unilateral Problems with Degenerate Coercivity
Loading...
Date
2023-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
University of M'sila
Abstract
In this work we study the existence and regularity of the solutions of unilateral problems
8>><>>:
u ‚ 0, a.e.in ›,
hAu,u ¡ vi • R› f (u ¡ v),
8v 2 H1
0(›),v ‚ 0, a.e.in ›,
(1)
Here › is a bounded, open subset of RN , with N ¨ 2, and Au ˘ ¡di v(a(x,u)Du) with a(x,s) :
›£R ! R is a Carathéodory function, satisfying the following conditions:
fi
(1¯jsj)θ • a(x,s) • fl. (2)
for some real number θ such that.
0 • θ ˙ 1 (3)
for almost every x 2 ›, for every s 2 R, where fi and fl are positive constants. The objective of
this contribution is to study the existence and regularity of the solutions of unilateral problems (1)
associated to A under assumptions (2)-(3) and with data f belonging to various Lebesgue space
Lm(›) , for some m ¨ 1.
Description
Keywords
Unilateral Problems, Degenerate Coercivity, Existence, Regularity.