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Displaying 521 – 540 of 700

Surface integrals and harmonic functions.

Movshovich, Yevgenya (2005)

Journal of Inequalities and Applications [electronic only]

Symmetric and Zygmund measures in several variables

Evgueni Doubtsov, Artur Nicolau (2002)

Annales de l’institut Fourier

Let $ω : (0, \infty) \to (0, \infty)$ be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure $μ \in ℝ^{n}$ is called $ω$ -Zygmund if there exists a positive constant $C$ such that $| μ (Q_{+}) - μ (Q_{-}) | \leq C ω (ℓ (Q_{+})) | Q_{+} |$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size. Similarly, $μ$ is called an $ω$ - symmetric measure if there exists a positive constant $C$ such that $| μ (Q_{+}) / μ (Q_{-}) - 1 | \leq C ω (ℓ (Q_{+}))$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size, $ℓ (Q_{+}) = ℓ (Q_{-}) < 1$ . We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...

Symmetry for exterior elliptic problems and two conjectures in potential theory

Boyan Sirakov (2001)

Annales de l'I.H.P. Analyse non linéaire

Symmetry problems 2

N. S. Hoang, A. G. Ramm (2009)

Annales Polonici Mathematici

Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.

Szegő projections for Hardy spaces of monogenic functions and applications.

Bernstein, Swanhild, Lanzani, Loredana (2002)

International Journal of Mathematics and Mathematical Sciences

Tangential limits of monotone Sobolev functions.

Mizuta, Yoshihiro (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

Temps locaux et l'intégrale d'aire de Lusin

Richard F. Gundy (1984)

Séminaire de probabilités de Strasbourg

Teoremi di confronto di tipo Harnack per funzioni armoniche in domini con frontiera hölderiana

Fausto Ferrari (1998)

Bollettino dell'Unione Matematica Italiana

Teoremi di media e formole di maggiorazione relative alle funzioni biarmoniche

Gaetano Fichera (1978)

Rendiconti del Seminario Matematico della Università di Padova

The Absolute Continuity of Elliptic Measure Revisited.

Carlos E. Kenig, Jill Pipher (1998)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

The atomic decomposition of harmonic functions satisfying certain conditions of integrability.

Bogdan, Krzysztof (1995)

International Journal of Mathematics and Mathematical Sciences

The Besov capacity in metric spaces

Juho Nuutinen (2016)

Annales Polonici Mathematici

We study a capacity theory based on a definition of Hajłasz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are γ-medians, for which we also prove a new version of a Poincaré type inequality.

The boundary Harnack principle for the fractional Laplacian

Krzysztof Bogdan (1997)

Studia Mathematica

We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.

The boundary-value problems for Laplace equation and domains with nonsmooth boundary

Dagmar Medková (1998)

Archivum Mathematicum

Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.

Currently displaying 521 – 540 of 700