On maximum principles for solutions to nonlinear elliptic ODEs and radial solutions to nonlinear elliptic PDE's via Opial‐type inequalities
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DOI: 10.1002/mma.7055
Abstract: We consider degenerated nonlinear PDE of elliptic type: −div(a(|x|)|∇w(x)|p−2∇w(x))+h|x|,w(x),∇w(x),x|x|=ϕ(w(x)), a.e. in the ball in ℝn . Using the argument based on Opial‐type inequalities, we investigate qualitative properties of their radial solutions, like, for example, the… read more here.
Keywords: radial solutions; solutions nonlinear; type inequalities; opial type ... See more keywords
Existence of Solutions for Some Nonlinear Elliptic Equations in Musielak Spaces with Only the Log-Hölder Continuity Condition
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DOI: 10.1007/s00009-019-1466-z
Abstract: We study the existence of solutions for some nonlinear elliptic problems with $$L^1$$L1 data in Musielak spaces; we assume that the Musielak function satisfies only the log-Hölder continuity condition. read more here.
Keywords: solutions nonlinear; lder continuity; musielak spaces; nonlinear elliptic ... See more keywords
Gradient estimates of a nonlinear elliptic equation for the V-Laplacian
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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
Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s00205-021-01745-1
Abstract: This article is concerned with uniform $$C^{1,\alpha }$$ C 1 , α and $$C^{1,1}$$ C 1 , 1 estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis is based on the compactness method,… read more here.
Keywords: estimates periodic; fully nonlinear; homogenization; periodic homogenization ... See more keywords
Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s00220-019-03370-2
Abstract: In this paper we prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients. More precisely, we deal with coefficients and right hand sides (RHS) in Lq… read more here.
Keywords: regularity convex; fully nonlinear; regularity; elliptic equations ... See more keywords
Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s10915-017-0586-5
Abstract: We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated… read more here.
Keywords: fully nonlinear; difference; difference methods; higher order ... See more keywords
The first eigenvalue and eigenfunction of a nonlinear elliptic system
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DOI: 10.1016/j.apnum.2019.06.004
Abstract: In this paper, we study the first eigenvalue of a nonlinear elliptic system involving $p$-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically and numerically.… read more here.
Keywords: elliptic system; system; first eigenvalue; eigenvalue eigenfunction ... See more keywords
Riesz potential type estimates for nonlinear elliptic equations
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DOI: 10.1016/j.jde.2017.07.031
Abstract: Abstract For p ≥ 2 , we study nonlinear elliptic equations of p -Laplacian type with measure data div a ( D u , u , x ) = μ in Ω when the nonlinearity… read more here.
Keywords: riesz potential; potential type; type estimates; elliptic equations ... See more keywords
Analytic solutions of nonlinear elliptic equations on rectangular tori
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DOI: 10.1016/j.jde.2019.05.039
Abstract: In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove that these equations admit many analytic solutions. read more here.
Keywords: analytic solutions; equations rectangular; rectangular tori; solutions nonlinear ... See more keywords
The existence of solutions for nonlinear elliptic equations: Simple proofs and extensions of a paper by Y. Shi
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DOI: 10.1016/j.jde.2022.02.014
Abstract: The paper [Shi19] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. The results of [Shi19] include regularity assumptions on the perturbation and involve excluding parameters. The paper [Shi19] also constructs… read more here.
Keywords: paper; ill posed; problem; elliptic equations ... See more keywords
ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS
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DOI: 10.1017/s0004972720000702
Abstract: where Ω is a bounded domain, p ∈ (1,+∞) and f is a C nonlinearity. This equation is the nonlinear version of the widely studied semilinear elliptic equation −∆u = f (u) in a bounded… read more here.
Keywords: rigidity stable; stable solutions; elliptic problems; estimates rigidity ... See more keywords