Holder Continuity of Solutions to Degenerate Nondivergence Elliptic Equations of the Second Order

摘要

In a domain D c U" (n > 2) containing the origin, we consider the equation LU=∑from i=1 to n|x_i|~a_1u_x_ix_i=0 The goal of this work is to find the conditions on a, under which the solutions to Eq. (1) are Holder continuous in D. For linear uniformly elliptic equations with measurable coefficients, an internal a priori estimate for the Holder norm of solutions was proved in [1, 2]. Later, different proofs of this property were proposed in [3, 4]. The Holder continuity of solutions to certain degenerate equations was studied in [5]. The Holder norm of solutions to quasilinear equations was estimated in [6, 7]