Text only print
Full screen print
PDE Real Analysis Seminar
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|
2015/01/20
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Italo Capuzzo Dolcetta (Università degli Studi di Roma "La Sapienza")
Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators (English)
Italo Capuzzo Dolcetta (Università degli Studi di Roma "La Sapienza")
Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators (English)
[ Abstract ]
In my presentation I will report on a joint paper with H. Berestycki, A. Porretta and L. Rossi to appear shortly on JMPA.
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem.
The new notion of generalized principal eigenvalue that we introduce here allows us to deal with arbitrary type of degeneracy of the elliptic operators.
We further discuss the relations between this notion and other natural generalizations of the classical notion of principal eigenvalue, some of which have been previously introduced for particular classes of operators.
In my presentation I will report on a joint paper with H. Berestycki, A. Porretta and L. Rossi to appear shortly on JMPA.
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem.
The new notion of generalized principal eigenvalue that we introduce here allows us to deal with arbitrary type of degeneracy of the elliptic operators.
We further discuss the relations between this notion and other natural generalizations of the classical notion of principal eigenvalue, some of which have been previously introduced for particular classes of operators.
