THE REGULARITY OF SOLUTIONS TO SOME VARIATIONAL PROBLEMS, INCLUDING THE p-LAPLACE EQUATION FOR 2 ≤ p < 3

被引：17
作者：
Cellina, Arrigo [1 ]
机构：
[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via R Cozzi 53, I-20125 Milan, Italy
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2017年 / 23卷 / 04期
关键词：
Regularity of solutions to variational problems; p-harmonic functions; higher differentiability; ELLIPTIC-EQUATIONS; HARMONIC FUNCTIONS; SYSTEMS; DOMAINS;
D O I：
10.1051/cocv/2016064
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We consider the higher differentiability of solutions to the problem of minimizing integral(Omega)[L del u(x)) + g(x,v(x))]dx on u(0) + W-0(1,p)(Omega) where L(xi) = (l)(vertical bar xi vertical bar) = 1/p vertical bar xi vertical bar(p) and u(0) is an element of W-1,W-p(Omega). We show that, for 2 <= p < 3, under suitable regularity assumptions on g, there exists a solution u to the Euler- Lagrange equation associated to the minimization problem, such that del u is an element of W-loc(1,2)(Omega). In particular, for g(x, u) = f(x) u with f is an element of W-1,W-2(Omega) and 2 <= p < 3, any W-1,W-p(Omega) weak solution to the equation div(vertical bar del u vertical bar(p-2)del u) = f is in W-loc(2,2) (Omega).
引用
收藏
页码：1543 / 1553
页数：11
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