On the representation of the Green function of the Dirichlet problem and their properties for the polyharmonic equations

Koshanov, B. D.; Koshanova, Maira

doi:10.1063/1.4930446

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…Recall that the operator D −1 , appearing in (7), (8), is defined on 2l− the vector-functions U ∈ C 1,µ (D), satisfying the conditions (5). In terms of projector Q, acting according to the formula…”

Section: Fredholm Solvability Of the Problemmentioning

confidence: 99%

“…f 1 j = 0, 1 ≤ j ≤ 2l − 1, then any solution U problems (14) satisfies the condition (5). In other words, for the given right-hand side f 1 problem (14) is equivalent to (7), (8).…”

Section: Fredholm Solvability Of the Problemmentioning

confidence: 99%

“…In [2][3][4][5][6][7][8], an explicit form of the Green function of the Dirichlet problem for a polyharmonic equation in a multidimensional ball is constructed. The paper [9,10] is devoted to the investigation of the solvability of various boundary value problems for a polyharmonic equation in a multidimensional ball.…”

Section: Introductionmentioning

confidence: 99%

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On the solvability of the boundary value problems for the elliptic equation of high order on a plane

Koshanov¹,

Soldatov²

2018

Bul. Kar. Univ. - Math.

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On the solvability of the boundary value problems for the elliptic equation of high order on a plane For the elliptic equation of 2l−th order with of constant (and only) real coefficients we consider boundary value problem of the normal derivatives (kj − 1) order, j = 1,. .. , l, where 1 ≤ k1 <. .. < k l ≤ 2l − 1. When kj = j it moves into the Dirichlet problem, and when kj = j + 1 it moves into the Neumann problem. In this paper, the study is carried out in space C 2l,µ (D). We found the condition for Fredholm solvability of this problem and computed the index of this problem.

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Section: Fredholm Solvability Of the Problemmentioning

confidence: 99%

“…f 1 j = 0, 1 ≤ j ≤ 2l − 1, then any solution U problems (14) satisfies the condition (5). In other words, for the given right-hand side f 1 problem (14) is equivalent to (7), (8).…”

Section: Fredholm Solvability Of the Problemmentioning

confidence: 99%