Results 31 to 40 of about 2,945,859 (241)
A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient
Advanced Nonlinear Studies, 2020 We consider the elliptic equation -Δu=uq|∇u|p{-\Delta u=u^{q}|\nabla u|^{p}} in ℝn{\mathbb{R}^{n}} for any p>2{p>2} and q>0{q>0}. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant.
Filippucci Roberta +2 more
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Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees [PDF]
International Conference on Machine Learning, 2023 Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c>0$.
Anastasia Koloskova +2 more
semanticscholar +1 more source
Semilinear Elliptic Systems with Dependence on the Gradient [PDF]
Mediterranean Journal of Mathematics, 2018 We provide results on the existence, non-existence, multiplicity, and localization of positive radial solutions for semilinear elliptic systems with Dirichlet or Robin boundary conditions on an annulus. Our approach is topological and relies on the classical fixed point index. We present an example to illustrate our theory.
F. Cianciaruso, P. Pietramala
openaire +3 more sources
Quasilinear equations with dependence on the gradient
Nonlinear Analysis: Theory, Methods & Applications, 2009 Abstract We discuss the existence of positive solutions of the problem − ( q ( t ) φ ( u ′ ( t ) ) ) ′ = f ( t , u ( t ) , u ′ ( t ) ) for t ∈ ( 0 , 1 ) and u ( 0 ) = u ( 1 ) = 0 , where the nonlinearity f satisfies a superlinearity condition at 0 ...
Pedro Ubilla +3 more
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Confirming the Unusual Temperature Dependence of the Electric-Field Gradient in Zn
Crystals, 2022 The electric-field gradient (EFG) at nuclei in solids is a sensitive probe of the charge distribution. Experimental data, which previously only existed in insulators, have been available for metals with the development of nuclear measuring techniques ...
Heinz Haas +9 more
doaj +1 more source
Pressure-dependence of the aortic valve gradient
Journal of the American College of Cardiology, 1998 Dipendenza lineare el gradiente transaortico dalla pressione sistolica aortica e dalle resistenze ...
LEONI, LOIRA +6 more
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Training Neural Networks by Time-Fractional Gradient Descent
Axioms, 2022 Motivated by the weighted averaging method for training neural networks, we study the time-fractional gradient descent (TFGD) method based on the time-fractional gradient flow and explore the influence of memory dependence on neural network training. The
Jingyi Xie, Sirui Li
doaj +1 more source
On convergence of gradient-dependent integrands [PDF]
Applications of Mathematics, 2007 We study convergence properties of {υ(∇uk)}k∈ℕ if υ ∈ C(ℝm×m), |υ(s)| ⩽ C(1+|s|p), 1 < p < + ∞, has a finite quasiconvex envelope, uk → u weakly in W1,p (Ω; ℝm) and for some g ∈ C(Ω) it holds that ∫Ωg(x)υ(∇uk(x))dx → ∫Ωg(x)Qυ(∇u(x))dx as k → ∞. In particular, we give necessary and sufficient conditions for L1-weak convergence of {det ∇uk}k∈ℕ to det ∇u ...
openaire +2 more sources
Elastoplasticity of gradient-polyconvex materials [PDF]
, 2020 We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we prove the existence of the so-called energetic solution.
arxiv +1 more source
Robin problems for the p-Laplacian with gradient dependence
Discrete and Continuous Dynamical Systems. Series A, 2019 We consider a nonlinear elliptic equation with Robin boundary condition driven by the p-Laplacian and with a reaction term which depends also on the gradient.
G. Fragnelli +2 more
semanticscholar +1 more source