Green function estimates on complements of low-dimensional uniformly rectifiable sets. [PDF]
Math Ann, 2023 David G, Feneuil J, Mayboroda S.
europepmc +1 more source
A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems
Advances in Nonlinear Analysis, 2020 In this paper we deal with the elliptic ...
López-Martínez Salvador
doaj +1 more source
Bounds of Riesz Transforms on $L^p$ Spaces for Second Order Elliptic Operators [PDF]
arXiv, 2004 For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.
arxiv
The trace space of anisotropic least gradient functions depends on the anisotropy. [PDF]
Math Ann, 2023 Górny W.
europepmc +1 more source
On a nonlinear Robin problem with an absorption term on the boundary and L1 data
Advances in Nonlinear AnalysisWe deal with existence and uniqueness of nonnegative solutions to: −Δu=f(x),inΩ,∂u∂ν+λ(x)u=g(x)uη,on∂Ω,\left\{\begin{array}{ll}-\Delta u=f\left(x),\hspace{1.0em}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ \frac{\partial u}{\partial ...
Pietra Francesco Della +2 more
doaj +1 more source
The volume potential for elliptic differential operators in Schauder spaces [PDF]
arXivThe aim of this paper is to prove continuity results for the volume potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces of negative exponent and to generalize some classical results in Schauder spaces of positive exponents.
arxiv
Existence and continuation of solutions for a nonlinear Neumann problem [PDF]
arXiv, 2006 In this article we study the existence, continuation and bifurcation from infinity of nonconstant solutions for a nonlinear Neumann problem. We apply the Leray-Schauder degree and the degree for SO(2)-equivariant gradient operators defined by the second author.
arxiv
A new approach to solvability of some elliptic pde's with square integrable boundary data [PDF]
arXiv, 2008 This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.
arxiv
Advanced Nonlinear Studies, 2018 In this paper, we study the regularizing effect of lower order terms in elliptic problems involving a Hardy potential.
Arcoya David +2 more
doaj +1 more source
The Perron Method and the Non-Linear Plateau Problem [PDF]
arXiv, 2009 We describe a novel technique for solving the Plateau problem for constant curvature hypersurfaces based on recent work of Harvey and Lawson. This is illustrated by an existence theorem for hypersurfaces of constant Gaussian curvature in $\Bbb{R}^{n+1}$.
arxiv