On -harmonic functions
Thierry De Pauw (2007)
Journées Équations aux dérivées partielles
Similarity:
Thierry De Pauw (2007)
Journées Équations aux dérivées partielles
Similarity:
Piotr Fijałkowski (1992)
Annales Polonici Mathematici
Similarity:
We consider the existence of solutions of the system (*) , l = 1,...,k, in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.
Chunmei Wang (2014)
Applications of Mathematics
Similarity:
In this paper, we consider mortar-type Crouzeix-Raviart element discretizations for second order elliptic problems with discontinuous coefficients. A preconditioner for the FETI-DP method is proposed. We prove that the condition number of the preconditioned operator is bounded by , where and are mesh sizes. Finally, numerical tests are presented to verify the theoretical results.
Joachim Naumann, Jörg Wolf, Michael Wolff (1998)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We prove the interior Hölder continuity of weak solutions to parabolic systems (), where the coefficients are measurable in , Hölder continuous in and Lipschitz continuous in and .
Lahsen Aharouch, Youssef Akdim (2004)
Annales mathématiques Blaise Pascal
Similarity:
In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type where is a Leray-Lions operator and is a Carathéodory function having natural growth with respect to and satisfying the sign condition. The second term is such that, and .
Jun Wu (2000)
Acta Arithmetica
Similarity:
1. Introduction. Given x in (0,1], let x = [d₁(x),d₂(x),...] denote the Engel expansion of x, that is, (1) , where is a sequence of positive integers satisfying d₁(x) ≥ 2 and for j ≥ 1. (See [3].) In [3], János Galambos proved that for almost all x ∈ (0,1], (2) He conjectured ([3], P132) that the Hausdorff dimension of the set where (2) fails is one. In this paper, we prove this conjecture: Theorem. . We use L¹ to denote the one-dimensional Lebesgue measure on (0,1] and to denote...
Michael Levin (1995)
Fundamenta Mathematicae
Similarity:
Let X be a compactum and let be a countable family of pairs of disjoint subsets of X. Then A is said to be essential on Y ⊂ X if for every closed separating and the intersection is not empty. So A is inessential on Y if there exist closed separating and such that does not intersect Y. Properties of inessentiality are studied and applied to prove: Theorem. For every countable family of pairs of disjoint open subsets of a compactum X there exists an open set G ∩ X on...