A global second-order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains

Qianyun Miao; Fa Peng; Yuan Zhou

doi:10.1007/s00526-023-02538-y

A global second-order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains

Qianyun Miao
, Fa Peng^*
, Yuan Zhou

^*Corresponding author for this work

Beijing Institute of Technology
CAS - Academy of Mathematics and System Sciences
Beijing Normal University

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

5 Scopus citations

Abstract

Let Ω ⊂ Rⁿ be a bounded convex domain with n≥ 2 . Suppose that A is uniformly elliptic and belongs to W¹^,ⁿ when n≥ 3 or W¹^,^q for some q> 2 when n= 2 . For 1 < p< ∞ , we establish a global second-order regularity estimate ‖D[|Du|p-2Du]‖L2(Ω)+‖D[⟨ADu,Du⟩p-22ADu]‖L2(Ω)≤C‖f‖L2(Ω) for the inhomogeneous p-Laplace type equation -div(⟨ADu,Du⟩p-22ADu)=f in Ω with Dirichlet or Neumann homogeneous boundary condition. Similar result was also established for certain bounded Lipschitz domains whose boundary is weakly second-order differentiable and satisfies some smallness assumptions.

Original language	English
Article number	191
Journal	Calculus of Variations and Partial Differential Equations
Volume	62
Issue number	7
DOIs	https://doi.org/10.1007/s00526-023-02538-y
State	Published - Sep 2023
Externally published	Yes

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title = "A global second-order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains",

abstract = "Let Ω ⊂ Rn be a bounded convex domain with n≥ 2 . Suppose that A is uniformly elliptic and belongs to W1,n when n≥ 3 or W1,q for some q> 2 when n= 2 . For 1 < p< ∞ , we establish a global second-order regularity estimate ‖D[|Du|p-2Du]‖L2(Ω)+‖D[⟨ADu,Du⟩p-22ADu]‖L2(Ω)≤C‖f‖L2(Ω) for the inhomogeneous p-Laplace type equation -div(⟨ADu,Du⟩p-22ADu)=f in Ω with Dirichlet or Neumann homogeneous boundary condition. Similar result was also established for certain bounded Lipschitz domains whose boundary is weakly second-order differentiable and satisfies some smallness assumptions.",

author = "Qianyun Miao and Fa Peng and Yuan Zhou",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2023",

month = sep,

doi = "10.1007/s00526-023-02538-y",

language = "英语",

volume = "62",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

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TY - JOUR

T1 - A global second-order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains

AU - Miao, Qianyun

AU - Peng, Fa

AU - Zhou, Yuan

PY - 2023/9

Y1 - 2023/9

N2 - Let Ω ⊂ Rn be a bounded convex domain with n≥ 2 . Suppose that A is uniformly elliptic and belongs to W1,n when n≥ 3 or W1,q for some q> 2 when n= 2 . For 1 < p< ∞ , we establish a global second-order regularity estimate ‖D[|Du|p-2Du]‖L2(Ω)+‖D[⟨ADu,Du⟩p-22ADu]‖L2(Ω)≤C‖f‖L2(Ω) for the inhomogeneous p-Laplace type equation -div(⟨ADu,Du⟩p-22ADu)=f in Ω with Dirichlet or Neumann homogeneous boundary condition. Similar result was also established for certain bounded Lipschitz domains whose boundary is weakly second-order differentiable and satisfies some smallness assumptions.

AB - Let Ω ⊂ Rn be a bounded convex domain with n≥ 2 . Suppose that A is uniformly elliptic and belongs to W1,n when n≥ 3 or W1,q for some q> 2 when n= 2 . For 1 < p< ∞ , we establish a global second-order regularity estimate ‖D[|Du|p-2Du]‖L2(Ω)+‖D[⟨ADu,Du⟩p-22ADu]‖L2(Ω)≤C‖f‖L2(Ω) for the inhomogeneous p-Laplace type equation -div(⟨ADu,Du⟩p-22ADu)=f in Ω with Dirichlet or Neumann homogeneous boundary condition. Similar result was also established for certain bounded Lipschitz domains whose boundary is weakly second-order differentiable and satisfies some smallness assumptions.

UR - https://www.scopus.com/pages/publications/85164473488

U2 - 10.1007/s00526-023-02538-y

DO - 10.1007/s00526-023-02538-y

M3 - 文章

AN - SCOPUS:85164473488

SN - 0944-2669

VL - 62

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 7

M1 - 191

ER -

A global second-order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains

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