The Dirichlet problem for the biharmonic equation in a Lipschitz domain
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator , on an arbitrary bounded Lipschitz domain in . We establish existence and uniqueness results when the boundary values have first derivatives in , and the normal derivative is in . The resulting solution takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of is shown to be in .
The Dirichlet problem with non-compact boundary.
The Dirichlet space: a survey.
The Dynamics of Inner Functions. / Claus I. Doering; Ricardo Mané.
The evolution and Poisson kernels on nilpotent meta-abelian groups
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to , k>1. We consider a class of second order left-invariant differential operators on S of the form , where , and for each is left-invariant second order differential operator on N and , where Δ is the usual Laplacian on . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...
The fall of the doubling condition in Calderón-Zygmund theory.
The most important results of standard Calderón-Zygmund theory have recently been extended to very general non-homogeneous contexts. In this survey paper we describe these extensions and their striking applications to removability problems for bounded analytic functions. We also discuss some of the techniques that allow us to dispense with the doubling condition in dealing with singular integrals. Special attention is paid to the Cauchy Integral.[Proceedings of the 6th International Conference on...
The Fekete-Szegő theorem with splitting conditions: Part I
The Fekete-Szegő theorem with splitting conditions: Part II
The finite integral transform method for a parabolic differential equation on a graph.
The form boundedness criterion for the relativistic Schrödinger operator
We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
The Functional Equation
The General Riesz Decomposition and the Specific Order of Excessive Functions.
The Generalized Ahlfors-Heins Theorem in Certain d-Dimensional Cones.
The gradient lemma
We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
The Green formula and HP Spaces on trees.
The Harmonie Space Associated with a "Reasonable" Standard Process.
The heat and adjoint heat potentials
The Hölder duality for harmonic functions
The homogeneous transfinite diameter of a compact subset of
Let K be a compact subset of . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of is computed.