A REGULARITY RESULT FOR THE p-LAPLACIAN NEAR UNIFORM ELLIPTICITY

作者：Mercuri Carlo^*; Riey Giuseppe; Sciunzi Berardino

来源：SIAM Journal on Mathematical Analysis, 2016, 48(3): 2059-2075.

DOI：10.1137/16M1058546

• quasi-linear elliptic equations
• regularity theory
• degenerate elliptic equations

We consider weak solutions to a class of Dirichlet boundary value problems involving the p-Laplace operator, and prove that the second weak derivatives are in L-q with q as large as it is desirable, provided p is sufficiently close to p(0) = 2. We show that this phenomenon is driven by the classical Calderon-Zygmund constant. As a byproduct of our analysis we show that C-1,C-alpha regularity improves up to C-1,C-1-, when p is close enough to 2. This result we believe is particularly interesting in higher dimensions n > 2, when optimal C-1,C-alpha regularity is related to the optimal regularity of p-harmonic mappings, which is still open (see, e.g., E. Teixeira, Math. Ann., 358 (2014), pp. 241-256).

• 出版日期2016