Base and essential base in parabolic potential theory
Behaviour at the boundary of the complex Monge-Ampère equation
Besov capacity and Hausdorff measures in metric measure spaces.
Biharmonic Green domains in a Riemannian manifold
Let be a Riemannian manifold without a biharmonic Green function defined on it and a domain in . A necessary and sufficient condition is given for the existence of a biharmonic Green function on .
Biharmonic morphisms
Let and be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from to is a continuous map from to which preserves the biharmonic structures of and . In the present work we study this notion and characterize in some cases the biharmonic morphisms between and in terms of harmonic morphisms between the harmonic spaces associated with and and the coupling kernels of them.
Biholomorphic invariance of capacity and the capacity of an annulus
Bivariate Revuz measures and the Feynman-Kac formula
BMO and Lipschitz approximation by solutions of elliptic equations
We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.
Boundary behaviour of eigenfunctions of the Laplace operator on trees
Boundary behaviour of eigenfunctions of the Laplacian in a bi-tree.
Boundary estimates for derivatives of harmonic functions
Boundary Harnack principle for separated semihyperbolic repellers, harmonic measure applications.
Boundary potential theory for stable Lévy processes
We investigate properties of harmonic functions of the symmetric stable Lévy process on without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for...
Boundary value problems and layer potentials on manifolds with cylindrical ends
We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...
Bounded Analytic Functions in the Dirichlet Space.
Bounded holomorphic functions with multiple sheeted pluripolar hulls
We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.
Brownian motion on fractals and function spaces.