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On the semiregularity of boundary points for nonlinear equations
E. B. Frid
Abstract:
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.
Figures: 1.
Bibliography: 10 titles.
Received: 28.02.1973
Citation:
E. B. Frid, “On the semiregularity of boundary points for nonlinear equations”, Math. USSR-Sb., 23:4 (1974), 483–507
Linking options:
https://www.mathnet.ru/eng/sm3731https://doi.org/10.1070/SM1974v023n04ABEH001728 https://www.mathnet.ru/eng/sm/v136/i4/p516
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