On the interaction of boundary singular points in the Dirichlet problem for an elliptic equation with piecewise constant coefficients in a plane domain
Abstract:
For an elliptic equation in divergent form with a discontinuous scalar piecewise constant coefficient in an unbounded domain $\Omega\subset \mathbb{R}^2$ with a piecewise smooth noncompact boundary and smooth discontinuity lines of the coefficient, the $L_p$-interaction of a finite and an infinite singular points of a weak solution to the Dirichlet problem is studied in a class of functions with the first derivatives from $L_p(\Omega)$ in the entire range of the exponent $p\in(1,\infty)$.
Key words:elliptic equation in divergent form, discontinuous piecewise constant coefficient, unbounded domain, piecewise smooth noncompact boundary, smooth discontinuity lines of coefficient, Dirichlet problem, weak solution with the first derivatives from $L_p$, interaction of singularities.
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