Uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball
Sign Up to like & getrecommendations! Published in 2024 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.10031
Abstract: In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$ . Under suitable conditions, we prove that, for any given positive integer… read more here.
Keywords: nonlinear elliptic; elliptic equations; solutions nonlinear; uniqueness nodal ... See more keywords
Qualitative Stochastic Homogenization of Elliptic Equations With Random Coefficients and Convolutional Potentials
Sign Up to like & getrecommendations! Published in 2025 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.11182
Abstract: This paper deals with the homogenization problem for elliptic equations with random statistically homogeneous ergodic coefficients and convolutional potentials in bounded domains. Assuming that the potential has a small absolute expectation, we prove the almost… read more here.
Keywords: elliptic equations; homogenization; topology; equations random ... See more keywords
Sublinear Elliptic Equations with Unbounded Coefficients in Lipschitz Domains
Sign Up to like & getrecommendations! Published in 2024 at "Results in Mathematics"
DOI: 10.1007/s00025-024-02246-9
Abstract: This paper is concerned with the homogeneous Dirichlet problem for a sublinear elliptic equation with unbounded coefficients in a Lipschitz domain. Bilateral a priori estimates for positive solutions and a priori upper estimates for their… read more here.
Keywords: lipschitz domains; sublinear elliptic; elliptic equations; equations unbounded ... See more keywords
Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
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
Gradient estimates for nonlinear elliptic equations with first order terms
Sign Up to like & getrecommendations! Published in 2019 at "manuscripta mathematica"
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
A type of cascadic multigrid method for coupled semilinear elliptic equations
Sign Up to like & getrecommendations! Published in 2019 at "Numerical Algorithms"
DOI: 10.1007/s11075-019-00690-1
Abstract: This paper is to introduce a type of cascadic multigrid method for coupled semilinear elliptic equations. Instead of solving the coupled semilinear elliptic equation on a very fine finite element space directly, the new scheme… read more here.
Keywords: cascadic multigrid; multigrid method; method coupled; coupled semilinear ... See more keywords
Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces
Sign Up to like & getrecommendations! Published in 2020 at "Positivity"
DOI: 10.1007/s11117-020-00789-z
Abstract: In this paper, we prove existence, uniqueness, and local regularity of the solution to the Sobolev–Dirichlet problem for quasilinear elliptic equations in the generalized Orlicz–Sobolev spaces on domains, not necessarily bounded, of $${\mathbb {R}}^N$$ .… read more here.
Keywords: sobolev dirichlet; dirichlet problem; elliptic equations; problem quasilinear ... See more keywords
Gradient estimates for a class of quasilinear elliptic equations with measure data
Sign Up to like & getrecommendations! Published in 2018 at "Science China Mathematics"
DOI: 10.1007/s11425-017-9205-y
Abstract: We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the… read more here.
Keywords: class; measure; elliptic equations; measure data ... See more keywords
Multiplicity of solutions for elliptic equations involving fractional operator and sign-changing nonlinearity
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Pseudo-differential Operators and Applications"
DOI: 10.1007/s11868-020-00357-9
Abstract: In this work, we study the existence and the multiplicity of non-negative solutions for the following problem $$\begin{aligned} ({\mathrm{P}}_\uplambda ) \left\{ \begin{array}{ll} \mathcal {L} u = a(x) u^{q}+ \lambda b(x) u^p\quad \text {in }\Omega ,… read more here.
Keywords: multiplicity; lambda; multiplicity solutions; elliptic equations ... See more keywords
Existence and multiplicity of positive solutions to quasilinear elliptic equations with two parameters
Sign Up to like & getrecommendations! Published in 2017 at "Afrika Matematika"
DOI: 10.1007/s13370-016-0444-x
Abstract: In this paper, we are concerned with quasilinear elliptic equations with a Dirichlet boundary condition and two parameters. Using the truncation techniques and variational methods, the existence and/or multiplicity of positive solutions to the problems… read more here.
Keywords: existence multiplicity; positive solutions; elliptic equations; two parameters ... See more keywords
Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
Sign Up to like & getrecommendations! Published in 2020 at "Bulletin of The Iranian Mathematical Society"
DOI: 10.1007/s41980-020-00466-7
Abstract: The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alt ... read more here.
Keywords: dirichlet robin; analysis dirichlet; cauchy problem; elliptic equations ... See more keywords