A remark on the definitions of viscosity solutions for the integro-differential equations with L{é}vy operators
Abstract
The equivalence of three different definitions of viscosity solutions for the integro-differential equation with the L{é}vy operator is shown in this paper. The key is Lemma 2.1, in which we construct a sequence of the approximating test functions.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2010
- DOI:
- arXiv:
- arXiv:1012.3094
- Bibcode:
- 2010arXiv1012.3094A
- Keywords:
-
- Mathematics - Analysis of PDEs
- E-Print:
- J. Maths. Pures et Appl., 89, (2008), pp. 567-574