90 research outputs found
On -estimates for a class of non-local elliptic equations
We consider non-local elliptic operators with kernel
, where is a constant and is a
bounded measurable function. By using a purely analytic method, we prove the
continuity of the non-local operator from the Bessel potential space
to , and the unique strong solvability of the corresponding
non-local elliptic equations in spaces. As a byproduct, we also obtain
interior -estimates. The novelty of our results is that the function
is not necessarily to be homogeneous, regular, or symmetric. An application of
our result is the uniqueness for the martingale problem associated to the
operator .Comment: Minor revision, to appear in J. Funct. Ana
The Stochastic Heat Equation Driven by a Gaussian Noise: germ Markov Property
Let be the process
solution of the stochastic heat equation
driven by a Gaussian noise , which is white in time and has spatial
covariance induced by the kernel . In this paper we prove that the process
is locally germ Markov, if is the Bessel kernel of order \alpha=2k,k
\in \bN_{+}, or is the Riesz kernel of order \alpha=4k,k \in \bN_{+}.Comment: 20 page
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