Results 21 to 30 of about 5,040,927 (317)
On a new fractional Sobolev space with variable exponent on complete manifolds
Boundary Value Problems, 2022 We present the theory of a new fractional Sobolev space in complete manifolds with variable exponent. As a result, we investigate some of our new space’s qualitative properties, such as completeness, reflexivity, separability, and density.
A. Aberqi +3 more
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Every superposition operator mapping one Sobolev space into another is continuous
, 1979 Moshe Marcus, Victor J. Mizel
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Nonzero positive solutions of fractional Laplacian systems with functional terms
Mathematische Nachrichten, Volume 296, Issue 1, Page 102-121, January 2023., 2023 Abstract We study the existence of nonzero positive solutions of a class of systems of differential equations driven by fractional powers of the Laplacian. Our approach is based on the notion of fixed point index, and allows us to deal with nonlocal functional weights and functional boundary conditions. We present two examples to shed light on the type
Stefano Biagi +2 more
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Leray-Schauder’s solution for a nonlocal problem in a fractional Orlicz-Sobolev space
Moroccan Journal of Pure and Applied Analysis, 2020 Via Leray-Schauder’s nonlinear alternative, we obtain the existence of a weak solution for a nonlocal problem driven by an operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions.
A. Boumazourh, M. Srati
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Rendiconti Lincei, Matematica e Applicazioni, 2022 We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on \mathbb{R}^n n, using sizes of superlevel sets of suitable difference quotients. This provides an alternative point of view to the BBM formula by Bourgain, Brezis, and Mironescu, and ...
Brezis, Haïm +3 more
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On a New Parabolic Sobolev Embedding Map
Moroccan Journal of Pure and Applied Analysis, 2023 The purpose of the present article is to provide a new parabolic Sobolev embedding map between a parabolic weighted Sobolev space and the space of square-integrable functions on a cylinder. Furthermore, the embedding constant is furnished explicitly.
El Aidi Mohammed
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Numerical Linear Algebra with Applications, Volume 30, Issue 1, January 2023., 2023 Abstract In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B‐spline collocation method. For an arbitrary polynomial degree p$$ p $$, we show that the resulting coefficient matrices possess a Toeplitz‐like structure. We investigate their spectral properties via their symbol and we prove that, like for
Mariarosa Mazza +3 more
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Deep learning phase‐field model for brittle fractures
International Journal for Numerical Methods in Engineering, Volume 124, Issue 3, Page 620-638, 15 February 2023., 2023 Abstract We present deep learning phase‐field models for brittle fracture. A variety of physics‐informed neural networks (PINNs) techniques, for example, original PINNs, variational PINNs (VPINNs), and variational energy PINNs (VE‐PINNs) are utilized to solve brittle phase‐field problems.
Yousef Ghaffari Motlagh +2 more
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International Journal for Numerical Methods in Engineering, Volume 124, Issue 3, Page 714-751, 15 February 2023., 2023 Abstract In this work we present a novel monolithic Finite Element method for the hydroelastic analysis of very large floating structures (VLFS) with arbitrary shapes that is stable, energy conserving, and overcomes the need of an iterative algorithm. The new formulation enables a fully monolithic solution of the linear free‐surface flow, described by ...
Oriol Colomés +2 more
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Stochastic homogenization on perforated domains II – Application to nonlinear elasticity models
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 102, Issue 12, December 2022., 2022 Abstract Based on a recent work that exposed the lack of uniformly bounded W1,p→W1,p$W^{1,p}\rightarrow W^{1,p}$ extension operators on randomly perforated domains, we study stochastic homogenization of nonlinear p‐elasticity, 1
Martin Heida
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