On the polyharmonic Neumann problem in weighted spaces

Matevossian, Hovik A.

doi:10.1080/17476933.2017.1409740

Cited by 24 publications

(6 citation statements)

References 19 publications

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“…The second-order equation of this type is also used for solving the planar problem of finding the stress-strain state of a body of rectangular cross section with a cylindrical cavity along which an ideal incompressible fluid moves [22]. Papers [23][24][25] are also worth mentioning. In them, the asymptotic expansions of the solutions of the main boundary-value problems for the elasticity system and the biharmonic (polyharmonic) equation in the exterior of a compact set and in a half-space, including that in the form of a conormal asymptotics, were obtained.…”

Section: The Main Resultsmentioning

confidence: 99%

Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point

Korovina¹

2020

Mathematics

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This study is devoted to the description of the asymptotic expansions of solutions of linear ordinary differential equations with holomorphic coefficients in the neighborhood of an infinitely distant singular point. This is a classical problem of analytical theory of differential equations and an important particular case of the general Poincare problem on constructing the asymptotics of solutions of linear ordinary differential equations with holomorphic coefficients in the neighborhoods of irregular singular points. In this study we consider such equations for which the principal symbol of the differential operator has multiple roots. The asymptotics of a solution for the case of equations with simple roots of the principal symbol were constructed earlier.

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Section: The Main Resultsmentioning

confidence: 99%

Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point

Korovina¹

2020

Mathematics

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“…Imposing the same constraint on the behavior of the solution at infinity in various classes of unbounded domains, the author [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] studied the uniqueness (non-uniqueness) problem and found the dimensions of the spaces of solutions of boundary value problems for the elasticity system and the biharmonic (polyharmonic) equation.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics and Uniqueness of Solutions of the Elasticity System with the Mixed Dirichlet–Robin Boundary Conditions

Matevossian

2020

Mathematics

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We study properties of generalized solutions of the Dirichlet–Robin problem for an elasticity system in the exterior of a compact, as well as the asymptotic behavior of solutions of this mixed problem at infinity, with the condition that the energy integral with the weight |x|a is finite. Depending on the value of the parameter a, we have proved uniqueness (or non-uniqueness) theorems for the mixed Dirichlet–Robin problem, and also given exact formulas for the dimension of the space of solutions. The main method for studying the problem under consideration is the variational principle, which assumes the minimization of the corresponding functional in the class of admissible functions.

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“…In various classes of unbounded domains with finite weighted Dirichlet (energy) integral, one of the author [10][11][12][13][14][15][16][17][18][19][20][21][22][23] studied uniqueness (non-uniqueness) problem and found the dimensions of the spaces of solutions of boundary value problems for the elasticity system and the biharmonic (polyharmonic) equation.…”

Section: Introductionmentioning

confidence: 99%

Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains

Matevossian¹

2020

Journal of Siberian Federal University. Mathematics &Amp; Physics

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We study the unique solvability of the mixed Dirichlet-Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions of the mixed Dirichlet-Neumann problem

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On the polyharmonic Neumann problem in weighted spaces

Cited by 24 publications

References 19 publications

Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point

Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point

Asymptotics and Uniqueness of Solutions of the Elasticity System with the Mixed Dirichlet–Robin Boundary Conditions

Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains

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