Abstract
The paper is concerned with the properties of the solution to a Dirichlet problem for a homogeneous second-order elliptic equation with -boundary function, . The same conditions are imposed on the coefficients of the equation and the boundary of the bounded domain as were used to establish the solvability of this problem. The -norm of the nontangential maximal function is estimated in terms of the -norm of the boundary value. This result depends on a new estimate, proved below, for the nontangential maximal function in terms of an analogue of the Lusin area integral. Bibliography: 31 titles.
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