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
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
A type of cascadic multigrid method for coupled semilinear elliptic equations
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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
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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
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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
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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
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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
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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
Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations
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DOI: 10.1016/j.aim.2022.108279
Abstract: We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulæ… read more here.
Keywords: strong unique; elliptic equations; fractional elliptic; local asymptotics ... 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
Harnack inequality for quasilinear elliptic equations on Riemannian manifolds
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DOI: 10.1016/j.jde.2017.10.003
Abstract: Abstract We study viscosity solutions to degenerate and singular elliptic equations div ( F ′ ( | ∇ u | ) | ∇ u | ∇ u ) = h of p-Laplacian type on Riemannian… read more here.
Keywords: harnack inequality; inequality quasilinear; elliptic equations; riemannian manifolds ... See more keywords