Global second order Sobolev-regularity of p-harmonic functions

Akseli Haarala; Saara Sarsa

doi:10.1016/j.jde.2022.08.022

Global second order Sobolev-regularity of p-harmonic functions

Akseli Haarala, Saara Sarsa

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

We prove a global version of the classical result that p-harmonic functions belong to W-loc(2,2) for 1 < p < 3 + 2/n-2. The proof relies on Cordes' matrix inequalities [7] and techniques from the work of Cianchi and Maz'ya [5,6].

Original language	English
Journal	Journal of Differential Equations
Volume	339
Pages (from-to)	232-260
Number of pages	29
ISSN	0022-0396
DOIs	https://doi.org/10.1016/j.jde.2022.08.022
Publication status	Published - 5 Dec 2022
MoE publication type	A1 Journal article-refereed

Fields of Science

111 Mathematics
Global Sobolev regularity
p-Harmonic function

Access to Document

10.1016/j.jde.2022.08.022Licence: CC BY

1-s2.0-S0022039622004946-mainFinal published version, 399 KBLicence: CC BY

Cite this

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title = "Global second order Sobolev-regularity of p-harmonic functions",

abstract = "We prove a global version of the classical result that p-harmonic functions belong to W-loc(2,2) for 1 < p < 3 + 2/n-2. The proof relies on Cordes' matrix inequalities [7] and techniques from the work of Cianchi and Maz'ya [5,6].",

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AU - Sarsa, Saara

PY - 2022/12/5

Y1 - 2022/12/5

N2 - We prove a global version of the classical result that p-harmonic functions belong to W-loc(2,2) for 1 < p < 3 + 2/n-2. The proof relies on Cordes' matrix inequalities [7] and techniques from the work of Cianchi and Maz'ya [5,6].

AB - We prove a global version of the classical result that p-harmonic functions belong to W-loc(2,2) for 1 < p < 3 + 2/n-2. The proof relies on Cordes' matrix inequalities [7] and techniques from the work of Cianchi and Maz'ya [5,6].

KW - 111 Mathematics

KW - Global Sobolev regularity

KW - p-Harmonic function

U2 - 10.1016/j.jde.2022.08.022

DO - 10.1016/j.jde.2022.08.022

M3 - Article

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VL - 339

SP - 232

EP - 260

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -