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Displaying 41 – 60 of 76

On $L^{p}$ -solutions of the Laplace equation and zeros of holomorphic functions

Joaquim Bruna, Joaquim Ortega-Cerdà (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the dimension of $p$ -harmonic measure in space

John L. Lewis, Kaj Nyström, Andrew Vogel (2013)

Journal of the European Mathematical Society

Let $Ω \subset ℝ^{n}, n \geq 3$ , and let $p, 1 < p < \infty, p \neq 2$ , be given. In this paper we study the dimension of $p$ -harmonic measures that arise from non-negative solutions to the $p$ -Laplace equation, vanishing on a portion of $\partial Ω$ , in the setting of $δ$ -Reifenberg flat domains. We prove, for $p \geq n$ , that there exists $\tilde{δ} = \tilde{δ} (p, n) > 0$ small such that if $Ω$ is a $δ$ -Reifenberg flat domain with $δ < \tilde{δ}$ , then $p$ -harmonic measure is concentrated on a set of $σ$ -finite $H^{n - 1}$ -measure. We prove, for $p \geq n$ , that for sufficiently flat Wolff snowflakes the Hausdorff dimension of $p$ -harmonic measure...

On the existence of solutions to a fourth-order quasilinear resonant problem.

Liu, Shibo, Squassina, Marco (2002)

Abstract and Applied Analysis

On the Regularity of the Solution of the Biharmonic Variational Inequality.

Jens Frehse (1973)

Manuscripta mathematica

Optimal conditions for anti-maximum principles

Hans-Christoph Grunau, Guido Sweers (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Parapolicity and existence of bounded biharmonic functions

Cecilia Wang, LeoSario (1972)

Commentarii mathematici Helvetici

Perturbation of a biharmonic eigenvalue problem

Zaman, F.D. (1977)

Portugaliae mathematica

p-harmonic equation and quasiregular mappings

B. Bojarski, T. Iwaniec (1987)

Banach Center Publications

Principe du minimum et préfaisceau maximaux

Denis Feyel, Arnaud de La Pradelle (1971/1972)

Séminaire Brelot-Choquet-Deny. Théorie du potentiel

Pythagorean identity for polyharmonic polynomials.

Fryant, Allan, Vemuri, Murali Krishna (2002)

International Journal of Mathematics and Mathematical Sciences

Quasiharmonic $L^{p}$ -functions on riemannian manifolds

Lung Ock Chung, Leo Sario, Cecilia Wang (1975)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Regularity of p-harmonic functions on the plane.

Tadeusz Iwaniec, Juan J. Manfredi (1989)

Revista Matemática Iberoamericana

Remarks on some fourth order variational inequalities

H. Brézis, G. Stampacchia (1977)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.)

El Kadiri, Mohamed, Haddad, Sabah (2005)

International Journal of Mathematics and Mathematical Sciences

Reproducing kernels for Dunkl polyharmonic polynomials

Kamel Touahri (2012)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree $n$ and Dunkl polyharmonic of degree $m$ , i.e. $Δ_{k}^{m} u = 0$ , $m \in ℕ ∖ {0}$ , where $Δ_{k}$ 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

Lung Ock Chung, Leo Sario, Cecilia Wang (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I

Karel Rektorys, Jana Danešová, Jiří Matyska, Čestmír Vitner (1977)

Aplikace matematiky

Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II

Karel Rektorys, Jana Danešová, Jiří Matyska, Čestmír Vitner (1977)

Aplikace matematiky

Some constructions of biharmonic maps on the warped product manifolds

Abdelmadjid Bennouar, Seddik Ouakkas (2017)

Commentationes Mathematicae Universitatis Carolinae

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

H. Begehr, Yu. Dubinskiĭ (2001)

Colloquium Mathematicae

Two kinds of orthogonal decompositions of the Sobolev space W̊₂¹ and hence also of $W ₂^{- 1}$ for bounded domains are given. They originate from a decomposition of W̊₂¹ into the orthogonal sum of the subspace of the $Δ^{k}$ -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 $Δ^{k}$ -solenoidal...

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