Vladimir Maz'ya
On the fast computation of high dimensional volume potentials.
Wed, 11/04/2009 - 16:01 — SomNambulAuthors: Vladimir Maz'ya, Flavia Lanzara, Gunther Schmidt
Subjects: Numerical Analysis
AbstractA fast method of an arbitrary high order for approximating volume potentials
is proposed, which is effective also in high dimensional cases. Basis functions
introduced in the theory of approximate approximations are used. Results of
numerical experiments, which show approximation order O(h^8) for the Newton
potential in high dimensions, for example, for n= 200 000, are provided. The
computation time scales linearly in the space dimension. New one-dimensional
integral representations with separable integrands of the potentials of
advection-diffusion and heat equations are obtained.A quasi-commutativity property of the Poisson and composition operators.
Mon, 11/02/2009 - 16:01 — SomNambulAuthors: Vladimir Maz'ya, Alberto Cialdea
Subjects: Analysis of PDEs
AbstractLet $\Phi$ be a real valued function of one real variable, let $L$ denote an
elliptic second order formally self-adjoint differential operator with bounded
measurable coefficients, and let $P$ stand for the Poisson operator for $L$. A
necessary and sufficient condition on $\Phi ensuring the equivalence of the
Dirichlet integrals of $\Phi\circ Ph$ and $P(\Phi\circ h)$ is obtained. We
illustrate this result by some sharp inequalities for harmonic functions.Optimal estimates for the gradient of harmonic functions in the multidimensional half-space.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Gershon Kresin, Vladimir Maz'ya
Subjects: Analysis of PDEs
AbstractA representation of the sharp constant in a pointwise estimate of the
gradient of a harmonic function in a multidimensional half-space is obtained
under the assumption that function's boundary values belong to $L^p$. This
representation is concretized for the cases $p=1, 2,$ and $\infty$.Optimal estimates for the gradient of harmonic functions in the multidimensional half-space.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Gershon Kresin, Vladimir Maz'ya
Subjects: Analysis of PDEs
AbstractA representation of the sharp constant in a pointwise estimate of the
gradient of a harmonic function in a multidimensional half-space is obtained
under the assumption that function's boundary values belong to $L^p$. This
representation is concretized for the cases $p=1, 2,$ and $\infty$.
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