We suggest a method to solve boundary and initial-boundary value problems for a class of nonlinear parabolic equations with the infinite dimensional L'evy Laplacian $\Delta _L$ $$f\Bigl(U(t,x),\frac{\partial U(t,x)}{\partial t},\Delta_LU(t,x)\Bigl)=0$$ in fundamental domains of a Hilbert space.
S. Albeverio, Ya. Belopolskaya, and M. Feller, Boundary problems for fully nonlinear parabolic equations with Lévy Laplacian, Methods Funct. Anal. Topology 14
(2008), no. 1, 1-9.
BibTex
@article {MFAT441,
AUTHOR = {Albeverio, S. and Belopolskaya, Ya. and Feller, M.},
TITLE = {Boundary problems for fully nonlinear parabolic equations with Lévy Laplacian},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {1},
PAGES = {1-9},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=441},
}