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The regularity of solutions to some variational problems, including the <i>p</i>-Laplace equation for 2 ≤ <i>p</i>< 3
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, …