Boundary continuity for quasiminimizers on metric spaces
The paper considers a generalization of the variational problem \[ \int_\Omega|\nabla u(x)|^p dx\to\min,\quad u\in W^{1,p}_0(\Omega)+ w, \] on Sobolev type spaces on metric measure spaces [see, e.g., \textit{B. Franchi}, \textit{P. Hajlasz} and \textit{P. Koskela}, ``Definition of Sobolev classes on metric spaces'', Ann. Inst. Fourier 49, 1903-1924 (1999; Zbl 0938.46037)], and gives some sufficient conditions for boundary continuity (Hölder continuity) of quasiminimizers.
scientific article; zbMATH DE number 1839951