Volume 23, Number 4, October-December 2017
|Page(s)||1543 - 1553|
|Published online||21 September 2017|
The regularity of solutions to some variational problems, including the p-Laplace equation for 2 ≤ p< 3
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy.
Received: 1 February 2016
Revised: 6 July 2016
Accepted: 18 September 2016
We consider the higher differentiability of solutions to the problem of minimizing where L(|ξ|)=1/p|ξ|p and u0 ∈ W1,p(Ω). 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 In particular, for g(x,u) = f(x)u with f ∈ W1,2(Ω) and 2 ≤ p< 3, any W1,p(Ω) weak solution to the equation is in W2,2loc(Ω).
Mathematics Subject Classification: 49K10
Key words: Regularity of solutions to variational problems – p-harmonic functions – higher differentiability
© EDP Sciences, SMAI 2017
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