ON THE BEST HÖLDER EXPONENTS FOR GENERALIZED SOLUTIONS OF THE DIRICHLET PROBLEM FOR A SECOND ORDER ELLIPTIC EQUATION
Владимир Александрович Кондратьев, I Kopachek, O A Oleĭnik · Mathematics of the USSR-Sbornik · 1988
The authors study the behavior of generalized solutions of the Dirichlet problem for a second order elliptic equation in a neighborhood of a boundary point. Under certain assumptions on the structure of the boundary of the domain in such a neighborhood, and on the coefficients of the equation, a power modulus of continuity is obtained at the boundary point for generalized solutions of the Dirichlet problem, the exponent being best possible for domains with the indicated structure of the boundary near that point. The assumptions on the coefficients of the equation are essential, as an example shows. With the help of the indicated results on the modulus of continuity at boundary points, it is then shown that generalized solutions belong to Holder spaces in the closure of the domain, the Holder exponent again being best possible for the class of domains under consideration.Bibliography: 8 titles.