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A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
Mathematics, 2020 The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems.
Dumitru Motreanu +2 more
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Dependence of bacterial chemotaxis on gradient shape and adaptation rate.
PLoS Computational Biology, 2008 Simulation of cellular behavior on multiple scales requires models that are sufficiently detailed to capture central intracellular processes but at the same time enable the simulation of entire cell populations in a computationally cheap way.
Nikita Vladimirov +3 more
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Semilinear elliptic equations with dependence on the gradient
Electronic Journal of Differential Equations, 2012 In this article we consider elliptic equations whose nonlinear term depends on the gradient of the unknown. We assume that the nonlinearity has a asymptotically linear growth at zero and at infinity with respect to the second variable.
Guanggang Liu, Shaoyun Shi, Yucheng Wei
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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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Singular quasilinear elliptic systems with gradient dependence [PDF]
Positivity, 2022 In this paper, we prove existence and regularity of positive solutions for singular quasilinear elliptic systems involving gradient terms. Our approach is based on comparison properties, a priori estimates and Schauder's fixed point theorem.
Halima Dellouche, Abdelkrim Moussaoui
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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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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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Semilinear Elliptic Systems with Dependence on the Gradient [PDF]
Mediterranean Journal of Mathematics, 2018 The authors prove existence and multiplicity results for radial solutions of semilinear elliptic systems with full gradient dependence that are subject to boundary values problems on an annulus. The approach relies on the fixed point index.
F. Cianciaruso, P. Pietramala
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Polarization-dependent tunneling of light in gradient optics [PDF]
Physical Review E, 2007 Reflection-refraction properties of photonic barriers, formed by dielectric gradient nanofilms, for inclined incidence of both S- and P-polarized electromagnetic (EM) waves are examined by means of exactly solvable models. We present generalized Fresnel formulae, describing the influence of the non-local dispersion on reflectance and transmittance of ...
Shvartsburg, Alexander +2 more
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