Results 21 to 30 of about 3,188,796 (338)
Multidimensional encoding of restricted and anisotropic diffusion by double rotation of the q vector [PDF]
Magnetic Resonance, 2023 Diffusion NMR and MRI methods building on the classic pulsed gradient spin-echo sequence are sensitive to many aspects of translational motion, including time and frequency dependence (“restriction”), anisotropy, and flow, leading to ambiguities when ...
H. Jiang, L. Svenningsson, D. Topgaard
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Gradient system with dependence on the gradient at nonlinearity [PDF]
Applied Mathematical Sciences, 2013 In this paper we establish existence of solutions for quasilinear elliptic system of gradient form with dependence on the gradient at nonlinearity.
Rua Gabriel Monteiro da Silva +1 more
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Singular quasilinear convective elliptic systems in ℝN
Advances in Nonlinear Analysis, 2022 The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates.
Guarnotta Umberto +2 more
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The $p$-weak gradient depends on $p$ [PDF]
Proceedings of the American Mathematical Society, 2015 Given a>0, we construct a weighted Lebesgue measure on R^n for which the family of non constant curves has p-modulus zero for p\leq 1+a but the weight is a Muckenhoupt A_p weight for p>1+a. In particular, the p-weak gradient is trivial for small p but non trivial for large p. This answers an open question posed by several authors.
di Marino S., Speight G.
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On the relaxation of integral functionals depending on the symmetrized gradient [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020 AbstractWe prove results on the relaxation and weak* lower semicontinuity of integral functionals of the form$${\cal F}[u]: = \int_\Omega f \left( {\displaystyle{1 \over 2}\left( {\nabla u(x) + \nabla u{(x)}^T} \right)} \right) \,{\rm d}x,\quad u:\Omega \subset {\mathbb R}^d\to {\mathbb R}^d,$$over the space BD(Ω) of functions of bounded deformation or
Kosiba, Kamil, Rindler, Filip
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Some recent results on singular p-Laplacian equations
Demonstratio Mathematica, 2022 A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions.
Guarnotta Umberto +2 more
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Gradient estimates for nonlinear elliptic equations with a gradient-dependent nonlinearity [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2019 AbstractIn this paper, we obtain gradient estimates of the positive solutions to weightedp-Laplacian type equations with a gradient-dependent nonlinearity of the form0.1$${\rm div }( \vert x \vert ^\sigma \vert \nabla u \vert ^{p-2}\nabla u) = \vert x \vert ^{-\tau }u^q \vert \nabla u \vert ^m\quad {\rm in}\;\Omega^*: = \Omega {\rm \setminus }\{ 0\} .$$
Joshua Ching, Florica C. Cîrstea
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On a Singular Robin Problem with Convection Terms
Advanced Nonlinear Studies, 2020 In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established.
Guarnotta Umberto +2 more
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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
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Material dependence of Casimir forces: gradient expansion beyond proximity [PDF]
, 2011 A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA).
Casimir H. B. G. +6 more
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