Boundary problems for fully nonlinear parabolic equations with Lévy Laplacian

Authors

  • M. N. Feller 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. I. Belopolskaya St. Petersburg State University for Architecture and Civil Engineering, 2-ja Krasnoarmejskaja 4, St. Petersburg, 190005, Russia https://orcid.org/0000-0002-8303-2571
  • S. Albeverio Obolonsky prospect 7, ap. 108, Kyiv, 04205, Ukraine

DOI:

Keywords:

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

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.

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Published

2008-03-25

Issue

Vol. 14 No. 1 (2008)

Section

Articles

How to Cite

Feller, M. N., et al. “Boundary Problems for Fully Nonlinear Parabolic Equations With Lévy Laplacian”. Methods of Functional Analysis and Topology, vol. 14, no. 1, Mar. 2008, pp. 1-9, https://zen.imath.kiev.ua/index.php/mfat/article/view/365.