Abstract
The paper continues the construction of the \({{L}_{p}}\)-theory of elliptic Dirichlet and Neumann boundary value problems with discontinuous piecewise constant coefficients in divergent form for an unbounded domain \(\Omega \subset {{\mathbb{R}}^{2}}\) with a piecewise \({{C}^{1}}\) smooth noncompact Lipschitz boundary and \({{C}^{1}}\) smooth discontinuity lines of the coefficients. An earlier constructed \({{L}_{p}}\)-theory is generalized to the case of different smallest eigenvalues corresponding to a finite and an infinite singular point, and the effect of their interaction is further studied in the class of functions with first derivatives from \({{L}_{p}}(\Omega )\) in the entire range of the exponent \(p \in (1,\infty )\).
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REFERENCES
A. M. Bogovskii and V. N. Denisov, “On the interaction of boundary singular points in the Dirichlet problem for an elliptic equation with piecewise constant coefficients in a plane domain,” Comput. Math. Math. Phys. 59 (12), 2145–2163 (2019).
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Translated by I. Ruzanova
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Bogovskii, A.M. Interaction of Boundary Singular Points in an Elliptic Boundary Value Problem. Comput. Math. and Math. Phys. 63, 1664–1670 (2023). https://doi.org/10.1134/S096554252309004X
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DOI: https://doi.org/10.1134/S096554252309004X