Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Hua Chen,Wuhan University
Inviter:
李竞
Title:
Multiplicity and Regularity of Solutions for Infinitely Degenerate Elliptic Equations with a Free Perturbation
Time & Venue:
2015.8.27 16:00-17:00 N613
Abstract:
In this talk, we study the Dirichlet problem for a class of infinitely degenerate elliptic equations with a free perturbation. By using the logarithmic Sobolev inequality, perturbation theorem and Ekeland's variational principle, we obtain the existence of the infinitely many weak solutions and the existence of the nonnegative weak solution. Furthermore, by the methods of iteration and regularity theorems of degenerate elliptic equations, we can also prove the boundedness of the weak solutions and $C^{\infty}$-regularity of the nonnegative weak solution.