Some Extremal Problems for Solutions of the Modified Helmholtz Equation in the Half-Space

Gershon Kresin; Tehiya Ben Yaakov

doi:10.1007/978-981-16-6297-3_12

Some Extremal Problems for Solutions of the Modified Helmholtz Equation in the Half-Space

Gershon Kresin, Tehiya Ben Yaakov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Representations for the sharp coefficients in pointwise estimates involving the gradient of the solution to the modified Helmholtz equation (Δ- c²) u= 0 in the half-space R+n are described. It is assumed that the boundary data of the Dirichlet and Neumann problems in R+n belong to the space L^p. Each of these representations includes an extremal problem with respect to a vector parameter inside of an integral over the unit sphere in Rⁿ. Explicit formulas for solutions to the extremal problems are indicated for p∈ [ 2, ∞] and p∈ [ 2, (n+ 2 ) / 2 ] in the cases of Dirichlet and Neumann boundary data, respectively.

Original language	English
Title of host publication	Functional Differential Equations and Applications - FDEA-2019
Editors	Alexander Domoshnitsky, Alexander Rasin, Seshadev Padhi
Pages	171-176
Number of pages	6
DOIs	https://doi.org/10.1007/978-981-16-6297-3_12
State	Published - 2021
Event	7th International Conference on Functional Differential Equations and Applications, FDEA 2019 - Ariel, Israel Duration: 22 Aug 2019 → 27 Aug 2019

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	379
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	7th International Conference on Functional Differential Equations and Applications, FDEA 2019
Country/Territory	Israel
City	Ariel
Period	22/08/19 → 27/08/19

Keywords

Extremal problems
Half-space
Modified Helmholtz equation

Access to Document

10.1007/978-981-16-6297-3_12

Cite this

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title = "Some Extremal Problems for Solutions of the Modified Helmholtz Equation in the Half-Space",

abstract = "Representations for the sharp coefficients in pointwise estimates involving the gradient of the solution to the modified Helmholtz equation (Δ- c2) u= 0 in the half-space R+n are described. It is assumed that the boundary data of the Dirichlet and Neumann problems in R+n belong to the space Lp. Each of these representations includes an extremal problem with respect to a vector parameter inside of an integral over the unit sphere in Rn. Explicit formulas for solutions to the extremal problems are indicated for p∈ [ 2, ∞] and p∈ [ 2, (n+ 2 ) / 2 ] in the cases of Dirichlet and Neumann boundary data, respectively.",

keywords = "Extremal problems, Half-space, Modified Helmholtz equation",

author = "Gershon Kresin and Yaakov, {Tehiya Ben}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.; 7th International Conference on Functional Differential Equations and Applications, FDEA 2019 ; Conference date: 22-08-2019 Through 27-08-2019",

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doi = "10.1007/978-981-16-6297-3_12",

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Kresin, G & Yaakov, TB 2021, Some Extremal Problems for Solutions of the Modified Helmholtz Equation in the Half-Space. in A Domoshnitsky, A Rasin & S Padhi (eds), Functional Differential Equations and Applications - FDEA-2019. Springer Proceedings in Mathematics and Statistics, vol. 379, pp. 171-176, 7th International Conference on Functional Differential Equations and Applications, FDEA 2019, Ariel, Israel, 22/08/19. https://doi.org/10.1007/978-981-16-6297-3_12

Some Extremal Problems for Solutions of the Modified Helmholtz Equation in the Half-Space. / Kresin, Gershon; Yaakov, Tehiya Ben.
Functional Differential Equations and Applications - FDEA-2019. ed. / Alexander Domoshnitsky; Alexander Rasin; Seshadev Padhi. 2021. p. 171-176 (Springer Proceedings in Mathematics and Statistics; Vol. 379).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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