Speaker
Antonella Nastasi
Abstract
We study quasiminimizers of the following anisotropic energy (p, q) – Dirichlet integral
int_Omega ag_u^p dmu + int_omega bg_u^q dmu
in metric measure spaces, with g_u the minimal q-weak upper gradient of u. Here, Omegain X is an open bounded set, where (X, d, µ) is a complete metric measure space with metric d and a doubling Borel regular measure µ, supporting a weak (1, p)-Poincar´e inequality for 1 < p < q. We consider some coefficient functions a and b to be measurable and satisfying 0 References [1] A. Björn, J. Björn, Nonlinear potential theory on metric spaces, EMS Tracts in Mathematics, 17, European Mathematical Society (EMS), Zurich (2011). [2] V. Bögelein, F. Duzaar, P. Marcellini, C. Scheven, A variational approach to doubly nonlinear equations, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 29 (2018), 739–772. [3] J. Kinnunen, N. Shanmugalingam, Regularity of quasi-minimizers on metric spaces, Manuscripta Math., 105 (2001), 401–423. [4] P. Marcellini, Growth conditions and regularity for weak solutions to nonlinear elliptic pdes, J. Math. Anal. Appl., 501 (2021), https://doi.org/10.1016/j.jmaa.2020.124408. [5] A. Nastasi, C. Pacchiano Camacho, Regularity properties for quasiminimizers of a (p, q)- Dirichlet integral, Calc. Var., 227 (60) (2021).