A new approach to the L^p-theory of -\Delta + b\grad, and its applications to Feller processes with general drifts

Tuesday, March 15, 2016 - 2:00pm
Math Sci 111
Damir Kinzebulatov
(Indiana University Bloomington)

Abstract: We develop a detailed regularity theory of -\Delta +b\grad,
b:R^d -> R^d (d >= 3), in L^p for a wide class of vector fields b
combining, for the first time, critical point and critical hypersurface
singularities, and not reachable by the standard techniques of
perturbation theory. The L^p-theory allows us to construct associated
strong Feller process in C_\infty(R^d).
     Our starting object is an operator-valued function,  which, we
prove, determines the resolvent of an operator realization of -\Delta +
b\grad, the generator of a holomorphic C_0-semigroup on L^p(R^d). Then
the very form of the operator-valued function yields crucial information
about smoothness of the domain of the generator.

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