Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals
Abstract
Abstract We prove the higher differentiability of integer order of locally bounded minimizers of integral functionals of the form $$\begin{aligned} \mathcal {F}(u,\Omega ):= \,\sum _{i=1}^{n} \dfrac{1}{p_i}\displaystyle \int _\Omega \, a_i(x) |u_{x_i} |^{p_i} dx- \int _\Omega \omega (x)u(x) dx, \end{aligned}$$ F ( u , Ω ) : = ∑ i = 1 n 1 p i ∫ Ω a i ( x ) | u x i | p i d x - ∫ Ω ω ( x ) u ( x ) d x , where the exponents $$ p_i \ge 2 $$ p i ≥ 2 and the coefficients $$ a_i(x) $$ a i ( x ) satisfy a suitable Sobolev regularity. The main novelty consists in dealing with non-autonomous, anisotropic functionals, which depend also on the solution.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Optimization and Variational Analysis
Publication details
- Journal / source
- Ricerche di Matematica
- Volume
- 75
- Issue
- 2
- Pages
- 1017–1053
- Publication date
- 6 March 2026
- Language
- EN