We study the regularity of vector-valued local minimizers in W 1,p, p > 1, of the integral functional u → ∫ Ω [(μ2 + |Du|2)p/2 + f(x, u, |Du|)] dx, where Ω is an open set in ℝN and f is a continuous function, convex with respect to the last variable, such that 0 ≤ f(x, u, t) ≤ C(1 + tp). We prove that if f = f(x, t), or f = f(x, u, t) and p ≥ N, then local minimizers are locally Hölder continuous for any exponent less than 1. If f = f(x, u, t) and p < N then local minimizers are Hölder continuous for every exponent less than 1 in an open set Ω0 such that the Hausdorff dimension of Ω/Ω0 is less than N - p.
Cupini G., Petti R. (2003). Hölder continuity of local minimizers of vectorial integral functional. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 10(3), 269-285 [10.1007/s00030-003-1025-x].
Hölder continuity of local minimizers of vectorial integral functional
Cupini G.
;
2003
Abstract
We study the regularity of vector-valued local minimizers in W 1,p, p > 1, of the integral functional u → ∫ Ω [(μ2 + |Du|2)p/2 + f(x, u, |Du|)] dx, where Ω is an open set in ℝN and f is a continuous function, convex with respect to the last variable, such that 0 ≤ f(x, u, t) ≤ C(1 + tp). We prove that if f = f(x, t), or f = f(x, u, t) and p ≥ N, then local minimizers are locally Hölder continuous for any exponent less than 1. If f = f(x, u, t) and p < N then local minimizers are Hölder continuous for every exponent less than 1 in an open set Ω0 such that the Hausdorff dimension of Ω/Ω0 is less than N - p.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
