Boundary problems for fully nonlinear parabolic equations with Lévy Laplacian

Abstract

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.

Key words: L'evy Laplacian, nonlinear parabolic equations, boundary problems, initial-boundary value problems

Full Text

Article Information

Title	Boundary problems for fully nonlinear parabolic equations with Lévy Laplacian
Source	Methods Funct. Anal. Topology, Vol. 14 (2008), no. 1, 1-9
MathSciNet	MR2402148
Copyright	The Author(s) 2008 (CC BY-SA)

Authors Information

S. Albeverio
Institut fur Angewandte Mathematik, Universit ¨ at Bonn, Wegelerstr. 6, D–53115, Bonn, ¨ Germany; SFB 611, Bonn, Germany; BiBoS, Bielefeld, Germany; CERFIM, Locarno and USI, Switzerland 

Ya. Belopolskaya
St. Petersburg State University for Architecture and Civil Engineering, 2-ja Krasnoarmejskaja 4, St. Petersburg, 190005, Russia

M. Feller
Obolonsky prospect 7, ap. 108, Kyiv, 04205, Ukraine

Citation Example

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},
}