Distribution of primes and a weighted energy problem.
Distributions bi-sousharmoniques sur
L’object de ce travail est l’etude des fonctions fonctions localement sommable sur , vérifiant (où est Laplacien pris au sens des distributions) et que se comportent à l’infini comme des fonctions sousharmoniques. En parculier, nous caractérisons les fonctious qui sont à la fois bi-sousharmoniques et sousharmoniques.
Domain perturbations, capacity and shift of eigenvalues
After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator . If is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in Capacity in abstract Hilbert spaces and applications to higher order differential operators (Comm. P. D. E., 24:759–775,...
Double layer potential representation of the solution of the Dirichlet problem (Preliminary communication)
Double layer potentials and the Dirichlet problem
Double layer potentials on boundaries with corners and edges
Doubling conditions for harmonic measure in John domains
We introduce new classes of domains, i.e., semi-uniform domains and inner semi-uniform domains. Both of them are intermediate between the class of John domains and the class of uniform domains. Under the capacity density condition, we show that the harmonic measure of a John domain satisfies certain doubling conditions if and only if is a semi-uniform domain or an inner semi-uniform domain.
Duality and quasi-continuity for supermartingales
Duality and the Martin compactification
Let be a Bauer sheaf that admits a Green function. Then there exists a diffusion process corresponding to the sheaf whose resolvent possesses a Hunt-Kunita-Watanabe dual resolvent that comes from a diffusion process. If is a Brelot sheaf which possesses an adjoint sheaf the dual process corresponds to .The Martin compactification defined by a Brelot sheaf that admits a Green function coincides with a Kunita-Watanabe compactification defined by the dual resolvent.
Duality in the obstacle and unilateral problem for the biharmonic operator
The paper presents a problem of duality for the obstacle and unilateral biharmonic problem (the equilibrium of a thin plate with an obstacle inside the domain or on the boundary). The dual variational inequality is derived by introducing polar functions.