Global multi-Hölder estimate of solutions to elliptic equations of higher order
If P is an elliptic operator of m-th order on a given domain \(\Omega\), then the author [Acta Math. Sin., New Ser. 1, 382-387 (1985; Zbl 0627.35027)] proved that the m-th order elliptic equation with Dirichlet conditions \(D^ j_ nu=g_ j\), \(0\leq j\leq m/2-1\), \(Pu=f\) \((f\in C^{\gamma,\delta}(\Omega))\) implies \(u\in C^{m+{\bar \gamma},{\bar \delta}}(\Omega ')\) where \(\Omega '\subset \subset \Omega\) and \[ ({\tilde \gamma},{\tilde \delta})=(\gamma,\delta),\quad if\quad 0<\gamma <1,\quad \delta \in R';\quad =(\gamma,\delta -1),\quad if\quad \gamma =0,\quad \delta >1,\quad or\quad \gamma =1,\quad \delta \leq 0. \] The aim of this paper is to extend this multi-Hölder estimate to a boundary value problem. The global multi-Hölder estimate of solutions of this problem is obtained.
scientific article; zbMATH DE number 4111152