A Harnack inequality in Orlicz–Sobolev spaces

Arriagada, Waldo; Huentutripay, Jorge

doi:10.4064/sm8764-9-2017

Cited by 10 publications

(8 citation statements)

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“…al., they study the setting when what we call F , f are zero, and using Orlicz spaces they address additional difficulties including including different upper and lower (almost)-homogeneities of the integrand, while proving similar bounds to what we recovered here when f, F are both constantly zero. In the isotropic setting, [AH18] shows a Harnack inequality similar to the 3.5. Meanwhile [Toi12] proves a general Harnack inequality, while assuming that the terms like F , f are in L ∞ .…”

Section: Introductionmentioning

confidence: 89%

A Harnack inequality for weak solutions of the Finsler $γ$-Laplacian

Goering¹

2020

Preprint

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When 1 < γ < n, we study the regularity of W 1,γ -solutions of the anisotropic PDEBy focusing on the γ-homogeneity, we show that nonnegative subsolutions and supersolutions u are suitably bounded to ensure that full solutions are locally bounded. When u is nonnegative, this also implies a (weak) Harnack inequality. In the case when γ = 2, this includes divergence form uniformly elliptic PDEs in the special case when ρ(x, •) is assumed to be uniformly strongly convex. Analogous to the elliptic setting, when f, F ≡ 0, this ensures a Bernstein-type theorem for W 1,γ -solutions in R n .

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Section: Introductionmentioning

confidence: 89%

A Harnack inequality for weak solutions of the Finsler $γ$-Laplacian

Goering¹

2020

Preprint

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“…In this short note we present a parametric version of the estimates obtained in [2]. In this sense, the bounds obtained here are optimal.…”

Section: (L)mentioning

confidence: 97%

Improved bounds for solutions of ϕ-Laplacians

Arriagada¹,

Huentutripay²

2018

OpMath

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“…If additional, mild restrictions are imposed on g, we prove that solutions of this equation are regular, positive and vanish at infinity through an instrumental result (Theorem 3.1). The latter (which is consequence of an extended Harnack's inequality proved in [2]) states that the oscillation of the solutions is locally bounded by the supremum of the function on a ball. We stress the fact that φ need not be differentiable.…”

Section: Introductionmentioning

confidence: 94%

“…Choose any real nonnegative number L such that b ≤ φ(L). The following average estimate is proved in [2] for any p > 0 :…”

Section: The Property (P)mentioning

confidence: 99%