On the asymptotics near the piecewise smooth boundary of singular solutions of semilinear elliptic equations
We consider the problem (1) \(Lu = \sum^N_{i,j = 1} a_{ij} (x) u_{x_ix_j} + \sum^N_{i = 1} a_i (x) u_{x_i} - a(x) u = p(x) u^k\), \(u > 0\), \(x \in G\), \(\lim_{x \to \Gamma} u(x) = + \infty\), where \(G\) is a bounded domain whose boundary \(\Gamma\) is a piecewise smooth surface containing singularities of two types, conic points and edges; \(L\) is a uniformly elliptic operator in \(\overline G\); the coefficients of Eq. (1) belong to \(C^2 (\overline G)\); \(p(x) > 0\), \(a(x) \geq 0\), \(k > 1\), \(N \geq 2\). We obtain the asymptotics of the solution in the neighborhood of conic points and of edges of the boundary.
estimates for the second term of the asymptotics
scientific article; zbMATH DE number 830688