Results 51 to 60 of about 3,866,571 (229)

A Geometric Characterization of Steady Laminar Flow

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non‐contractible streamlines which foliate the domain), then they must be either parallel or circular flows.
Theodore D. Drivas, Marc Nualart
wiley   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Wavelets in a generalized Sobolev space [PDF]

, 2005
The generalized Sobolev space Hww(Rn) is defined as a generalization of the usual Sobolev space Hs(Rn). A multiresolution analysis for the generalized Sobolev space is developed. Wavelets orthogonal with respect to this space are constructed.
Pathak, R.S.
core   +1 more source

Kernel Bounds for Parabolic Operators Having First‐Order Degeneracy at the Boundary

Mathematische Nachrichten, EarlyView.
ABSTRACT We study kernel estimates for parabolic problems governed by singular elliptic operators ∑i,j=1N+1qijDij+cDyy,cγ+1>0,γ=qN+1,N+1,$$\begin{equation*} \sum _{i,j=1}^{N+1}q_{ij}D_{ij}+c\frac{D_y}{y},\qquad \frac{c}{\gamma }+1>0, \quad \gamma =q_{N+1,N+1}, \end{equation*}$$in the half‐space R+N+1={(x,y):x∈RN,y>0}$\mathbb {R}^{N+1}_+=\lbrace (x,y ...
L. Negro, C. Spina
wiley   +1 more source

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  

A Test Function Method for Weakly Coupled Systems With Derivative‐Type Nonlinearity

Mathematische Nachrichten, EarlyView.
ABSTRACT We consider a two by two system of inequalities which include fractional powers of the Laplace operator, coupled through a semilinear term of derivative type. We prove the nonexistence of global‐in‐time weak solutions for powers below the critical curve and possibly on the critical curve.
Marcello D'Abbicco, Antonio Lagioia
wiley   +1 more source

Sphere-Valued Sobolev Maps

, 2023
reservedAnalysis of the intrinsic properties of the Sobolev maps from the n-dimensional space to the k-dimensional ...
MASSERINI, SIMONE
core  

Boundedness of Composition Operators in Orlicz–Morrey Spaces

Mathematische Nachrichten, EarlyView.
ABSTRACT In this paper, we investigate the necessary and sufficient conditions for the boundedness of composition operators on Orlicz–Morrey spaces. Our results encompass Lebesgue and generalized Morrey spaces as special cases. In addition, we characterize the boundedness of composition operators on weak Orlicz–Morrey spaces, which include the Orlicz ...
Masahiro Ikeda, Isao Ishikawa, Ryota Kawasumi   +2 more
wiley   +1 more source

A weighted Hardy-Sobolev-Maz’ya inequality [PDF]

, 2014
We provide a weighted extension of a Hardy-Sobolev-Maz’ya inequality that is due to Filippas, Maz’ya and ...
Sourdis, Christos
core