An Agmon-Allegretto-Piepenbrink principle for Schrödinger operators. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2022 Buccheri S, Orsina L, Ponce AC.
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Lipschitz Interior regularity for the viscosity and weak solutions of the pseudo-$p$Laplacian [PDF]
arXiv, 2014 We prove interior Lipschitz regularity result for weak and viscosity solutions of the pseudo $p$Laplacien $(p-1)\sum_i |\partial_i u|^{p-2} \partial_{ii} u = f$ for $p>2$ and $f$ bounded.
arxiv
Operator compression with deep neural networks. [PDF]
Adv Contin Discret Model, 2022 Kröpfl F, Maier R, Peterseim D.
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Carleman Estimate for Surface in Euclidean Space at Infinity [PDF]
arXiv, 2017 This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads to rigidity results in geometry.
arxiv
Symmetry of n-mode positive solutions for two-dimensional H\'enon type systems
, 2013 We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities.
Shioji, Naoki, Squassina, Marco
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On the exterior Dirichlet problem for special Lagrangian equations [PDF]
arXiv, 2017 In this paper, we establish the existence and uniqueness theorem of the exterior Dirichlet problem for special Lagrangian equations with prescribed asymptotic behavior at infinity.
arxiv
On the uniqueness of a solution to a stationary convection-diffusion equation with a generalized divergence-free drift [PDF]
arXiv, 2017 In this paper we establish the uniqueness of a solution to a stationary convection-diffusion equation in divergence form with an exponentially summable generalized divergence-free drift.
arxiv
Maximum principles for Laplacian and fractional Laplacian with critical integrability
, 2019 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider $-\Delta u(x)+c(x)u(x)\geq 0$ in $B_1$ where $c(x)\in L^{p}(B_1)$, $B_1\subset \mathbf{R}^n$. As is known that $p=\frac{n}{2}$
Lü, Yingshu
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A Note on Lipschitz Continuiy of the Solutions of a Class of Elliptic Free Boundary Problems [PDF]
arXiv, 2019 We provide a new and simple proof based on Harnack's inequality to the Lipschitz continuity of the solutions of a class of free boundary problems.
arxiv
Infinity-Harmonic Potentials and Their Streamlines
, 2019 We consider certain solutions of the Infinity-Laplace Equation in planar convex rings. Their ascending streamlines are unique while the descending ones may bifurcate.
Lindgren, Erik, Lindqvist, Peter
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