Two-Operator Boundary-Domain Integral Equations for Variable Coefficient Dirichlet Problem in 2D

Ayele, Tsegaye G.; Bekele, Solomon

doi:10.1007/978-3-030-16077-7_5

Cited by 3 publications

(4 citation statements)

References 8 publications

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“…For the case a = b, the assertion is proved in Dufera and Mikhailov 5, Theorem 5 and the first relation in (22) together with 8, Theorem 8. 16 (ii) imply the proof for the case a ≠ b as well (see also 7,Theorem 2 ).…”

Section: Invertibility Of Single Layer Potentialmentioning

confidence: 64%

“…Note that if a = b, then, the last domain integral disappears, and the two-operator second Green identity (10) reduces to the one operator second Green identity (7).…”

Section: Definitionmentioning

confidence: 99%

“…As in previous studies, 3,4,7,13 we define the parametrix-based logarithmic and remainder potential operators as…”

Section: Parametrix and Parametrix-based Potential Operatorsmentioning

confidence: 99%

“…In this paper, extending the results in Ayele and Bekele, 7 the mixed (Dirichlet-Neumann) boundary value problem (BVP) for the linear second-order scalar elliptic differential equation with variable coefficients in a bounded two-dimensional domain is considered. The two-operator approach and appropriate parametrix (Levi function) are used to reduce this BVP to four systems of two-operator BDIEs denoted by M11, M12, M21, and M22.…”

Section: Introductionmentioning

confidence: 99%

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Two‐operator boundary‐domain integral equation systems for variable‐coefficient mixed Boundary Value Problem in 2D

Ayele

Bekele

2021

Math Methods in App Sciences

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In this paper, the mixed (Dirichlet-Neumann) boundary value problem (BVP) for the linear second-order scalar elliptic differential equation with variable coefficients in a bounded two-dimensional domain is considered. The two-operator approach and appropriate parametrix (Levi function) are used to reduce this BVP to four systems of two-operator boundary-domain integral equations (BDIEs).Although the theory of two-operator BDIEs in 3D is well developed, the BDIEs in 2D need a special consideration due to their different equivalence properties. As a result, we need to set conditions on the domain or on the associated Sobolev spaces to ensure the invertibility of corresponding parametrix-based integral layer potentials and hence the unique solvability of BDIEs. The equivalence of the two-operator BDIE systems to the original BVP is shown. The invertibility of the associated operators is proved in the appropriate Sobolev spaces.

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Section: Invertibility Of Single Layer Potentialmentioning

confidence: 64%

“…Note that if a = b, then, the last domain integral disappears, and the two-operator second Green identity (10) reduces to the one operator second Green identity (7).…”

Section: Definitionmentioning

confidence: 99%

“…As in previous studies, 3,4,7,13 we define the parametrix-based logarithmic and remainder potential operators as…”

Section: Parametrix and Parametrix-based Potential Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Two‐operator boundary‐domain integral equation systems for variable‐coefficient mixed Boundary Value Problem in 2D

Ayele

Bekele

2021

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract