On the existence of bounded generalized solutions of the Dirichlet problem for a class of nonlinear high-order elliptic equations

Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms

“…Existence and L ∞ -estimates of bounded solutions for quasilinear elliptic equations with natural growth of lower-order terms, in nondegenerate case, were established, for instance, in [2], [3], [7], [29], [30], [31], and the Hölder continuity on compact subsets of Ω of solutions was proved in [19,Chapter IX,Section 2], [32]. Similar results for elliptic equations and variational inequalities without the natural growth were obtained in [23], [25], [26] for the nondegenerate case, and also in [15]- [18], [22], [27], [28] for the degenerate case.…”