A parabolic partial differential equation ut′(t, x)= L u (t, x) is considered, where L is a linear
second-order differential operator with time-independent (but dependent on x) coefficients …

We present a general method of solving the Cauchy problem for multidimensional parabolic
(diffusion type) equation with variable coefficients which depend on spatial variable but do …

Linear differential equations in Banach spaces are closely connected with the concept of
one-parameter semigroups. In particular, this theory allows a detailed analysis of the initial …

We consider the diffusion semigroup P t associated to a class of degenerate elliptic
operators A\; on\; R^ n. This class includes the hypoelliptic Ornstein-Uhlenbeck operator but …

We prove two assumptions made in an article by Butko et al. concerning the existence of a
strongly continuous operator semigroup solving a Cauchy-Dirichlet problem for an elliptic …

Let A generate a strongly continuous contraction semigroup {T (t)} on a Hilbert space and let
L be a bounded operator. If L (ζ I− A)− 1 is compact, then the Cesàro limit of‖ LT (t) f‖ 2 (as …

Given a regular bounded domain, we show that an elliptic operator whose diffusion
coefficients degenerate at the boundary at least as the square of the distance from the …

In this paper, we show that a process modeled by a strongly continuous real‐valued
semigroup (that has a space convolution operator as infinitesimal generator) cannot satisfy …

It is well known that an important diffusion process is described with the help of the
differential operator whose domain includes the so-called Wentzell boundary conditions …

First, we study the regularity of the heat semigroup generated by the Operator H= L+ V
where V is a potential bounded from above, and L is the generator of the Ornstein …