# Ya. I. Belopolskaya

orcid.org/0000-0002-8303-2571
Search this author in Google Scholar

Articles: 6

### Boundary problems for the wave equation with the Lévy Laplacian in Shilov's class

Methods Funct. Anal. Topology 16 (2010), no. 3, 197-202

We present solutions to some boundary value and initial-boundary value problems for the "wave" equation with the infinite dimensional L\'evy Laplacian $\Delta _L$ $$\frac{\partial^2 U(t,x)}{\partial t^2}=\Delta_LU(t,x)$$ in the Shilov class of functions.

### Boundary problems for fully nonlinear parabolic equations with Lévy Laplacian

Methods Funct. Anal. Topology 14 (2008), no. 1, 1-9

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.

### Lévy-Dirichlet forms. II

Methods Funct. Anal. Topology 12 (2006), no. 4, 302-314

A Dirichlet form associated with the infinite dimensional symmetrized Levy-Laplace operator is constructed. It is shown that there exists a natural connection between this form and a Markov process. This correspondence is similar to that studied in a previous paper by the same authors for the non-symmetric Levy Laplacian.

### Riquier problem for nonlinear elliptic equations with Lévy Laplacians

Methods Funct. Anal. Topology 11 (2005), no. 1, 1-9

### Mathematical heritage of Yuri L'vovich Daletskii

Methods Funct. Anal. Topology 5 (1999), no. 4, 1-8

### Burgers equation on a Hilbert manifold and the motion of incompressible fluid

Ya. I. Belopolskaya

Methods Funct. Anal. Topology 5 (1999), no. 4, 15-27