Journal•ISSN: 0232-2064
Zeitschrift Fur Analysis Und Ihre Anwendungen
European Mathematical Society
About: Zeitschrift Fur Analysis Und Ihre Anwendungen is an academic journal published by European Mathematical Society. The journal publishes majorly in the area(s): Nonlinear system & Boundary value problem. It has an ISSN identifier of 0232-2064. Over the lifetime, 1496 publications have been published receiving 15852 citations. The journal is also known as: ZAA & Journal for analysis and its applications.
Topics: Nonlinear system, Boundary value problem, Operator theory, Differential equation, Sobolev space
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TL;DR: Theorem 2.7 as discussed by the authors generalizes a result of Gao and Xu [4] concerning the approximation of functions of bounded variation by linear combinations of a fixed sigmoidal function.
Abstract: We generalize a result of Gao and Xu [4] concerning the approximation of functions of bounded variation by linear combinations of a fixed sigmoidal function to the class of functions of bounded φ-variation (Theorem 2.7). Also, in the case of one variable, [1: Proposition 1] is improved. Our proofs are similar to that of [4].
1,316 citations
TL;DR: In this paper, a proof for the Poincaré inequality with explicit constant for convex domains is given, which is a modification of the original proof, which was valid only for the two-dimensional case.
Abstract: In this article a proof for the Poincaré inequality with explicit constant for convex domains is given. This proof is a modification of the original proof [5], which is valid only for the two-dimensional case.
228 citations
TL;DR: In this paper, the norms of the small and grand Lebesgue spaces depend only on the non-decreasing rearrangement of the underlying measure space, and they assume that the original measure space has measure 1.
Abstract: We give the following, equivalent, explicit expressions for the norms of the small and grand Lebesgue spaces, which depend only on the non-decreasing rearrangement (we assume here that the underlying measure space has measure 1):
209 citations
176 citations
TL;DR: In this article, the authors extend Caffarelli's result on interior W 2,p-estimates for viscosity solutions of uniformly elliptic equations and prove W 2 p-estimate at a flat boundary.
Abstract: In this paper we extend Caffarelli’s result on interior W 2,p-estimates for viscosity solutions of uniformly elliptic equations and prove W 2,p-estimates at a flat boundary. Moreover we extend a result of A. Świech and prove W 1,p-estimates at the boundary. Thereafter we combine these results and prove global W 2,p-estimates for equations with dependence on Du and u. Finally, we show that the previous estimates lead to an existence result for W 2,p-strong solutions.
151 citations