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
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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 - http://www.scopus.com/inward/record.url?scp=85164473488&partnerID=8YFLogxK
U2 - 10.1007/s00526-023-02538-y
DO - 10.1007/s00526-023-02538-y
M3 - Article
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 -