Results 31 to 40 of about 2,334 (153)

Variable Exponent Spaces of Differential Forms on Riemannian Manifold

Journal of Function Spaces and Applications, 2012
We introduce the Lebesgue space and the exterior Sobolev space for differential forms on Riemannian manifold 𝑀 which are the Lebesgue space and the Sobolev space of functions on 𝑀, respectively, when the degree of differential forms to be zero.
Yongqiang Fu, Lifeng Guo
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A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space

Comptes Rendus. Mathématique, 2020
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert.
Di Marino, Simone, Lučić, Danka, Pasqualetto, Enrico   +2 more
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Clarkson’s Inequalities for Periodic Sobolev Space [PDF]

Учёные записки Казанского университета: Серия Физико-математические науки, 2016
The paper is devoted to developing the proof of Clarkson's inequalities for periodic functions belonging to the Sobolev space. The norm of the space has not been considered earlier.
I.V. Korytov
doaj  

An approach to metric space-valued Sobolev maps via weak* derivatives

Analysis and Geometry in Metric Spaces
We give a characterization of metric space-valued Sobolev maps in terms of weak* derivatives. More precisely, we show that Sobolev maps with values in dual-to-separable Banach spaces can be defined in terms of classical weak derivatives in a weak* sense.
Creutz Paul, Evseev Nikita
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Polynomial differentiation decreases the training time complexity of physics-informed neural networks and strengthens their approximation power

Machine Learning: Science and Technology, 2023
We present novel approximates of variational losses, being applicable for the training of physics-informed neural networks (PINNs). The formulations reflect classic Sobolev space theory for partial differential equations (PDEs) and their weak ...
Juan-Esteban Suarez Cardona, Michael Hecht   +1 more
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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
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Fractional Maximal Functions in Metric Measure Spaces

Analysis and Geometry in Metric Spaces, 2013
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev ...
Heikkinen Toni, Lehrbäck Juha, Nuutinen Juho, Tuominen Heli   +3 more
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Trace principle for Riesz potentials on Herz-type spaces and applications

Journal of Inequalities and Applications
We establish trace inequalities for Riesz potentials on Herz-type spaces and examine the optimality of conditions imposed on specific parameters.
M. Ashraf Bhat, G. Sankara Raju Kosuru
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On the Space of Locally Sobolev-Slobodeckij Functions

Journal of Function Spaces, 2022
The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space. In this paper,
A. Behzadan, M. Holst
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Diffeomorphism Invariant Minimization of Functionals with Nonuniform Coercivity

Mathematics
We consider the minimization of a functional of the calculus of variations, under assumptions that are diffeomorphism invariant. In particular, a nonuniform coercivity condition needs to be considered.
Marco Degiovanni, Marco Marzocchi
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