Gradient estimates of a nonlinear elliptic equation for the V-Laplacian
Sign Up to like & getrecommendations! Published in 2019 at "Archiv der Mathematik"
DOI: 10.1007/s00013-019-01419-1
Abstract: This paper studies gradient estimates for positive solutions of the nonlinear elliptic equation $$\begin{aligned} \Delta _V(u^p)+\lambda u=0,\quad p\ge 1, \end{aligned}$$on a Riemannian manifold (M, g) with k-Bakry–Emery Ricci curvature bounded from below. We consider both the… read more here.
Keywords: gradient estimates; estimates nonlinear; nonlinear elliptic; elliptic equation ... See more keywords
Gradient estimates for nonlinear elliptic equations with first order terms
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DOI: 10.1007/s00229-020-01210-5
Abstract: We study existence and Lorentz regularity of distributional solutions to elliptic equations with measurable coefficients and either a convection or a drift first order term. The presence of such a term makes the problem not… read more here.
Keywords: gradient estimates; estimates nonlinear; elliptic equations; first order ... See more keywords
Uniform gradient estimates on manifolds with a boundary and applications
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DOI: 10.1007/s13324-018-0228-6
Abstract: We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperimetric inequalities, using Ledoux’s argument, and uniform quantitative gradient estimates, firstly… read more here.
Keywords: gradient estimates; manifolds boundary; uniform gradient; estimates manifolds ... See more keywords
Sharp pointwise gradient estimates for Riesz potentials with a bounded density
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DOI: 10.1007/s13324-018-0230-z
Abstract: We establish sharp inequalities for the Riesz potential and its gradient in $$\mathbb {R}^{n}$$Rn and indicate their usefulness for potential analysis, moment theory and other applications. read more here.
Keywords: gradient estimates; riesz potentials; sharp pointwise; estimates riesz ... See more keywords
Weighted gradient estimates for the class of very singular p-Laplace system
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DOI: 10.1016/j.jde.2020.08.039
Abstract: Abstract Let n ∈ { 2 , 3 , 4 , … } , N ∈ { 1 , 2 , 3 , … } and p ∈ ( 1 , 2 − 1 n… read more here.
Keywords: system; weighted gradient; laplace system; gradient estimates ... See more keywords
Sharp gradient estimates for quasilinear elliptic equations with $p(x)$ growth on nonsmooth domains
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2017.10.012
Abstract: In this paper, we study quasilinear elliptic equations with the nonlinearity modelled after the p(x) p ( x ) -Laplacian on nonsmooth domains and obtain sharp Calderon–Zygmund type estimates in the variable exponent setting. In… read more here.
Keywords: gradient estimates; estimates quasilinear; sharp gradient; nonsmooth domains ... See more keywords
Gradient estimates via the Wolff potentials for a class of quasilinear elliptic equations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.03.037
Abstract: Abstract In this paper we obtain the pointwise gradient estimates via the nonlinear Wolff potentials for weak solutions of a class of non-homogeneous quasilinear elliptic equations with measure data. read more here.
Keywords: gradient estimates; estimates via; class; elliptic equations ... See more keywords
Gradient estimates for semi-linear elliptic equations with prescribed contact angle problem
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.05.066
Abstract: Abstract In this paper, we find a new auxiliary function and use the maximum principle to give a new proof for the gradient of a solution for semi-linear elliptic equations with capillarity-type problem. read more here.
Keywords: gradient estimates; linear elliptic; semi linear; elliptic equations ... See more keywords
Local elliptic gradient estimates for a nonlinear parabolic equation under the Ricci flow
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.05.006
Abstract: Abstract In this study, we derive local elliptic (Hamilton type and Souplet–Zhang type) gradient estimates for positive solutions of the nonlinear parabolic partial differential equation ( Δ t − ∂ t ) u = q… read more here.
Keywords: ricci flow; gradient estimates; nonlinear parabolic; local elliptic ... See more keywords
Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-018-1705-z
Abstract: AbstractWe consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a smooth metric measure space (M,g,e−fdv)$(M, g,e^{-f}\,dv)$: Δfu+aulogu+bu=0,$$\Delta_{f} u+au\log u+bu=0, $$ where a, b are two real constants. When the ∞-Bakry–Émery… read more here.
Keywords: gradient estimates; nonlinear elliptic; elliptic equation; estimates liouville ... See more keywords
Gradient estimates for the Fisher–KPP equation on Riemannian manifolds
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DOI: 10.1186/s13661-018-0946-6
Abstract: In this paper, we consider positive solutions to the Fisher–KPP equation on complete Riemannian manifolds. We derive the gradient estimate. Using the estimate, we get the classic Harnack inequality which extends the recent result of… read more here.
Keywords: gradient estimates; kpp equation; riemannian manifolds; estimates fisher ... See more keywords