Boundary weak Harnack estimates and quantitative strong maximum principles for uniformly elliptic PDE

Boyan Sirakov

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Boundary weak Harnack estimates and quantitative strong maximum principles for uniformly elliptic PDE

Boyan Sirakov

Analysis of PDEs · Submitted 3 Aug 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give full boundary extensions to two fundamental estimates in the theory of elliptic PDE, the weak Harnack inequality and the quantitative strong maximum principle, for uniformly elliptic equations in non-divergence form.

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arXiv ID1608.01359 (version 3)

Pith IDWHUPB2BH, Pith's permanent record of this paper and its review

CitationBoyan Sirakov. "Boundary weak Harnack estimates and quantitative strong maximum principles for uniformly elliptic PDE." arXiv:1608.01359 (2016). https://pith.science/paper/WHUPB2BH

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We give full boundary extensions to two fundamental estimates in the theory of elliptic PDE, the weak Harnack inequality and the quantitative strong maximum principle, for uniformly elliptic equations in non-divergence form.

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s0	We give full boundary extensions to two fundamental estimates in the theory of elliptic PDE, the weak Harnack inequality and the quantitative strong maximum principle, for uniformly elliptic equations in non-divergence form.	contribution 0.98	0.94	0.91	asserted 1.00

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Original abstract

We give full boundary extensions to two fundamental estimates in the theory of elliptic PDE, the weak Harnack inequality and the quantitative strong maximum principle, for uniformly elliptic equations in non-divergence form.

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2 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Alternatively, the last estimate can be deduced in a standard fashion from the general Harnack inequality for $v/d$, proved in [ref] .

Results of Ambrosetti-Prodi type for non-selfadjoint elliptic operators · Proof of Proposition [ref] · 0.84

Compares with it 1 paper

For this context only, we present a simpler and alternative proof of a slightly weaker version of IHOL found in [ref] (see Theorem [ref] and Remark [ref] below) which is the same version found in [ref] .

Inhomogeneous Hopf-Ole\u{i}nik Lemma and Applications. Part IV: Sharp Krylov Boundary Gradient Type Estimates for Solutions to Fully Nonlinear Differential Inequalities with unbounded coefficients and $C^{1,Dini}$ boundary data · Introduction · 0.91

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This follows from Theorems 2 and 11 in [ref] .

Inhomogeneous Hopf-Ole\u{i}nik Lemma and Applications. Part IV: Sharp Krylov Boundary Gradient Type Estimates for Solutions to Fully Nonlinear Differential Inequalities with unbounded coefficients and $C^{1,Dini}$ boundary data · Main results · 0.96

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Cites as background 1 paper

Moreira that other applications of Theorem [ref] to regularity theory and free boundary problems are in preparation [ref] , [ref] .

Inhomogeneous Hopf-Ole\u{i}nik Lemma and Applications. Part IV: Sharp Krylov Boundary Gradient Type Estimates for Solutions to Fully Nonlinear Differential Inequalities with unbounded coefficients and $C^{1,Dini}$ boundary data · Introduction and Main Results · 0.82

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