On -solutions of the Laplace equation and zeros of holomorphic functions
On the dimension of -harmonic measure in space
Let , and let , be given. In this paper we study the dimension of -harmonic measures that arise from non-negative solutions to the -Laplace equation, vanishing on a portion of , in the setting of -Reifenberg flat domains. We prove, for , that there exists small such that if is a -Reifenberg flat domain with , then -harmonic measure is concentrated on a set of -finite -measure. We prove, for , that for sufficiently flat Wolff snowflakes the Hausdorff dimension of -harmonic measure...
On the existence of solutions to a fourth-order quasilinear resonant problem.
On the Regularity of the Solution of the Biharmonic Variational Inequality.
Optimal conditions for anti-maximum principles
Parapolicity and existence of bounded biharmonic functions
Perturbation of a biharmonic eigenvalue problem
p-harmonic equation and quasiregular mappings
Principe du minimum et préfaisceau maximaux
Pythagorean identity for polyharmonic polynomials.
Quasiharmonic -functions on riemannian manifolds
Regularity of p-harmonic functions on the plane.
Remarks on some fourth order variational inequalities
Remarks on the biharmonic Martin boundary and the integral representation of biharmonic functions. (Remarques sur la frontière de Martin biharmonique et la représentation intégrale des fonctions biharmoniques.)
Reproducing kernels for Dunkl polyharmonic polynomials
In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree and Dunkl polyharmonic of degree , i.e. , , where is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.
Riemannian manifolds with bounded Dirichlet finite polyharmonic functions
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II
Some constructions of biharmonic maps on the warped product manifolds
In this paper, we characterize a class of biharmonic maps from and between product manifolds in terms of the warping function. Examples are constructed when one of the factors is either Euclidean space or sphere.
Some orthogonal decompositions of Sobolev spaces and applications
Two kinds of orthogonal decompositions of the Sobolev space W̊₂¹ and hence also of for bounded domains are given. They originate from a decomposition of W̊₂¹ into the orthogonal sum of the subspace of the -solenoidal functions, k ≥ 1, and its explicitly given orthogonal complement. This decomposition is developed in the real as well as in the complex case. For the solenoidal subspace (k = 0) the decomposition appears in a little different form. In the second kind decomposition the -solenoidal...