This paper is devoted to the functional analytic approach to the problem of
construction of Feller semigroups with VentceP (Wentzell) boundary conditions.
The problem of construction of Feller semigroups has never before been studied in
the non-transversal case. In this paper we consider the non-transversal case, and
solve from the viewpoint of functional analysis the problem of construction of Feller
semigroups for elliptic Waldenfels operators. Intuitively, our result may be stated
as follows : One can construct a Feller semigroup corresponding to such a diffusion
phenomenon that a Markovian particle moves both by jumps and continuously in
the state space until it "dies" at which time it reaches the set where the absorption
phenomenon occurs.
1991 Mathematics Subject Classification. Primary 47D07, 35J25 ; Secondary
47D05, 60J35, 60J60.
Key words and phrases : Feller semigroups, Markov processes, elliptic boundary
value problems.
This research was partially supported by Grant-in-Aid for General Scientific
Research (No. 03640122), Ministry of Education, Science and Culture.
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