On the local Hölder continuity of the inverse of the $p$-Laplace operator

Lê, An

doi:10.1090/s0002-9939-07-08913-7

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2021

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Cited by 7 publications

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References 9 publications

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“…Since, w n is uniformly bounded in C 1,l (Ω) for some l ∈ (0, 1) and by using interpolation inequality [33,Corollary 1.3]) for any θ ∈ (0, 1), we get…”

Section: 1mentioning

confidence: 98%

Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities

Arora¹

2021

Preprint

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This paper is concerned with the study of multiple positive solutions to the following elliptic problem involving a nonhomogeneous operator with nonstandard growth of p-q type and singular nonlinearitieswhere Ω is a bounded domain inLp,qu := div(|∇u| p−2 ∇u + |∇u| q−2 ∇u), 1 < p < q < ∞, γ ∈ (0, 1), and f is a continuous nondecreasing map satisfying suitable conditions. By constructing two distinctive pairs of strict sub and super solution, and using fixed point theorems by Amann [1], we prove existence of three positive solutions in the positive cone of C δ (Ω) and in a certain range of λ.

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“…Since, w n is uniformly bounded in C 1,l (Ω) for some l ∈ (0, 1) and by using interpolation inequality [33,Corollary 1.3]) for any θ ∈ (0, 1), we get…”

Section: 1mentioning

confidence: 98%