Results 71 to 80 of about 4,761,041 (315)
Diffusive Resource–Consumer Dynamics With the Simplest Learning Mechanism and Nonlocal Memory Usage
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT To describe cognitive consumers' movement, we study a diffusive resource–consumer model with nonlocal memory usage described by a system of parabolic equations, which is coupled with spatial memory dynamics described by a linear learning equation.
Qigang Deng, Ranchao Wu, Hao Wang
wiley +1 more source
Compactness of higher-order Sobolev embeddings [PDF]
, 2012 We study higher-order compact Sobolev embeddings on a domain $\Omega \subseteq \mathbb R^n$ endowed with a probability measure $\nu$ and satisfying certain isoperimetric inequality.
Slavíková, Lenka
core
Abstract Boundary Delay Systems and Application to Network Flow
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This paper investigates the well‐posedness and positivity of solutions to a class of delayed transport equations on a network. The material flow is delayed at the vertices and along the edges. The problem is reformulated as an abstract boundary delay equation, and well‐posedness is proved by using the Staffans–Weiss theory.
András Bátkai +2 more
wiley +1 more source
Journal of Inequalities and Applications, 2011 Let , the authors introduce in this paper a class of the hypersingular Marcinkiewicz integrals along surface with variable kernels defined by , where with .
Ruiying Wei, Yin Li
doaj +2 more sources
Sobolev Embedding Theorem for the Sobolev-Morrey spaces
Қарағанды университетінің хабаршысы. Математика сериясы, 2016 In this paper we prove a Sobolev Embedding Theorem for Sobolev-Morrey spaces. The proof is based on the Sobolev Integral Representation Theorem and on a recent results on Riesz potentials in generalized Morrey spaces of Burenkov, Gogatishvili, Guliyev ...
V.I. Burenkov, N.A. Kydyrmina
doaj
Duality properties of metric Sobolev spaces and capacity
Mathematics in Engineering, 2021 We study the properties of the dual Sobolev space $H^{-1,q}(\mathbb{X})= \big(H^{1,p}(\mathbb{X})\big)'$ on a complete extended metric-topological measure space $\mathbb{X}=(X,\tau,\rm{d},\rm{m})$ for $p\in (1,\infty)$.
Luigi Ambrosio, Giuseppe Savaré
doaj +1 more source
G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE [PDF]
, 2014 We introduce a new notion of G-expectation-weighted Sobolev spaces, or in short, G-Sobolev spaces, and prove that a backward SDEs driven by G-Brownian motion are in fact path dependent PDEs in the corresponding Sobolev spaces under G-norms.
Peng, Shige, Song, Yongsheng
core
On the constants for multiplication in Sobolev spaces
Advances in Applied Mathematics, 2006 For n > d/2, the Sobolev (Bessel potential) space H^n(R^d, C) is known to be a Banach algebra with its standard norm || ||_n and the pointwise product; so, there is a best constant K_{n d} such that || f g ||_{n} <= K_{n d} || f ||_{n} || g ||_{n} for all f, g in this space.
C. Morosi, L. Pizzocchero
openaire +5 more sources
Optimal Control Applications and Methods, EarlyView.Optimal Control of AB Caputo Fractional Stochastic Integrodifferential Control System with Noninstantaneous Impulses. ABSTRACT This study is concerned with the existence of mild solution and optimal control for the Atangana–Baleanu fractional stochastic integrodifferential system with noninstantaneous impulses in Hilbert spaces. We verify the existence
Murugesan Johnson +2 more
wiley +1 more source
Sobolev spaces in the presence of symmetries
Journal de Mathématiques Pures et Appliquées, 1997 We prove that Sobolev embeddings can be improved in the presence of symmetries. This includes embeddings in higher \(L^p\)-spaces and compactness properties of these embeddings. While such phenomena have been observed in specific context by several authors, we treat here the case of arbitrary Riemannian manifolds (where, in particular, no global chart ...
Hebey, Emmanuel, Vaugon, Michel
openaire +4 more sources