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The Correct Definition of Second-Order Elliptic Operators with Point Interactions and their Resolvents

Abstract

A finite number of interior points is removed from an open bounded simply connected domain with smooth boundary in a multidimensional space. In the resulting domain, we consider correctly solvable boundary value problems for a second-order elliptic operator with variable coefficients. The domain of such problems may contain functions that have a singularity of the type of the fundamental solution and its partial derivatives.

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Funding

The work was partially supported by the Ministry of Education and Science of the Republic of Kazakhstan (grants AP05131292 and AP05131845).

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Correspondence to G. E. Abduakhitova or B. E. Kanguzhin.

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Abduakhitova, G.E., Kanguzhin, B.E. The Correct Definition of Second-Order Elliptic Operators with Point Interactions and their Resolvents. Sib. Adv. Math. 30, 153–161 (2020). https://doi.org/10.3103/S1055134420030013

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Keywords

  • uniformly elliptic operator
  • multiconnected domain
  • everywhere solvable boundary value problem
  • resolvent of an elliptic operator
  • Bitsadze–Samarskiĭ boundary value problem