On the semiregularity of boundary points for nonlinear equations

In the article the first boundary value problem is considered for boundedly inhomogeneous elliptic equations in a nonsmooth plane domain. It is established that an isolated point of the boundary can belong to one of four types: regular, semiregular from above or below (this means that the set of boundary values retained at the point has the form $[a,\infty)$ or $(-\infty,a]$ respectively) and nonregular. It is proved that the Dirichlet problem is equivalent to a certain problem with a free (on the set of semiregular points) boundary.
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