Optimal second-order regularity for the p-Laplace system

2018/10/18 by Cianchi, Andrea, Maz'ya, Vladimir · 2 citations
#35J25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.08144

Abstract

Second-order estimates are established for solutions to the p-Laplace system with right-hand side in L². The nonlinear expression of the gradient under the divergence operator is shown to belong to W^1,2, and hence to enjoy the best possible degree of regularity. Moreover, its norm in W^1,2 is proved to be equivalent to the norm of the right-hand side in L². Our global results apply to solutions to both Dirichlet and Neumann problems, and entail minimal regularity of the boundary of the domain. In particular, our conclusions hold for arbitrary bounded convex domains. Local estimates for local solutions are provided as well.

Cited by

• Existence results for variational quasilinear elliptic systems involving the vectorial p-Laplacian
• Second-order boundary estimates for solutions to a class of quasilinear elliptic equations

Related

• Optimal second order boundary regularity for solutions to p-Laplace equations
• Second-order regularity for parabolic p-Laplace problems
• Global Schauder estimates for the p-Laplace system
• A pointwise differential inequality and second-order regularity for nonlinear elliptic systems
• Global second order optimal regularity for the vectorial p-Laplacian