Kuwait Journal of Science

Previous Issues

Advance Search
Year : From To Vol
Issue Discipline:

Volume :24 Issue : 2 1997      Add To Cart                                                                    Download

High order regularity of the singularities of the solution of a parabolic equation in a singular domain


 Department of Mathematics, Ecole Normale Supêrieure, 16050-Kouba, Algiers, Algeria
(Note: Mathematical characters in this abstract are not shown properly in html format. Please send us an e-mail if you are interested in this paper)


We are concerned, in this work, with the parabolic equation:


in the following non convex polygonal domain ) described by the variables (t, x) e D

= (—1, 0) x (—1, 1) U [ 1) x (0, 1).

The boundary conditions are of Cauchy—Dirichlet type while the second member f of the equation lies in the non symmetric Sobolev space H” “(1 defined, for p e %J, by:

denotes the well known Lebesgue space.

.. satisfies some compatibility conditions, the “natural” space of solutions, in case of . enough (e.g., convex domain) is the Sobolev space “ 4 1)( According to some

‘ we know that the space of solutions may be different. In Sadallah (1996), we dealt with

 (*) for p = 0. Now, we are interested in the optimal regularity of the singularities .. appear in the solution when p is any integer.

. main result of this work shows the existence of 2(p + 1) singularities (vi, k)j=O, k=O p :: for all f e H” 4 satisfying some compatibility conditions, the solution belongs

1 4 l)(ç IRv k

in addition , the singularities fulfill the optimal regularity condition, for all j = 0, 1 and

V . k Hnj+k 4(rJ+k)( r . < 2j


Kuwait Journal of Science
Journal of Law

You are Visitor No.


Journal of Law
Journal of Law
Tell your friendsJournal of Law
Journal of Law

Last Updated

Jun 19, 2012

Journal of Law
Journal of Law
Journal of Law

Please enter your email Here to receive our news

Journal of Law