An extension problem related to the square root of the Laplacian with Neumann boundary condition

In this work we define the square root of the Laplacian operator with Neumann boundary condition via harmonic extension method. By using Fourier series and periodic even extension we define the non-local operator square root in three type of bounded domains such as an interval, square or a ball....

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Main Authors:	Michele de Oliveira Alves, Sergio Muniz Oliva
Format:	Article
Language:	English
Published:	Texas State University 2014-01-01
Series:	Electronic Journal of Differential Equations
Subjects:	Harmonic extension Neumann boundary condition square root of the Laplacian nonlinear problem
Online Access:	http://ejde.math.txstate.edu/Volumes/2014/12/abstr.html

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spelling	doaj-a8dea5872c6544b9915cb40728942d8b2020-11-25T00:24:13ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-01-01201412,118An extension problem related to the square root of the Laplacian with Neumann boundary conditionMichele de Oliveira Alves0Sergio Muniz Oliva1 Univ. Estadual de Londrina, Brazil Univ. de Sao Paulo, Brazil In this work we define the square root of the Laplacian operator with Neumann boundary condition via harmonic extension method. By using Fourier series and periodic even extension we define the non-local operator square root in three type of bounded domains such as an interval, square or a ball. Also, as application we study the existence of weak solutions for a class of nonlinear elliptic problems.http://ejde.math.txstate.edu/Volumes/2014/12/abstr.htmlHarmonic extensionNeumann boundary conditionsquare root of the Laplaciannonlinear problem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Michele de Oliveira Alves Sergio Muniz Oliva
spellingShingle	Michele de Oliveira Alves Sergio Muniz Oliva An extension problem related to the square root of the Laplacian with Neumann boundary condition Electronic Journal of Differential Equations Harmonic extension Neumann boundary condition square root of the Laplacian nonlinear problem
author_facet	Michele de Oliveira Alves Sergio Muniz Oliva
author_sort	Michele de Oliveira Alves
title	An extension problem related to the square root of the Laplacian with Neumann boundary condition
title_short	An extension problem related to the square root of the Laplacian with Neumann boundary condition
title_full	An extension problem related to the square root of the Laplacian with Neumann boundary condition
title_fullStr	An extension problem related to the square root of the Laplacian with Neumann boundary condition
title_full_unstemmed	An extension problem related to the square root of the Laplacian with Neumann boundary condition
title_sort	extension problem related to the square root of the laplacian with neumann boundary condition
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2014-01-01
description	In this work we define the square root of the Laplacian operator with Neumann boundary condition via harmonic extension method. By using Fourier series and periodic even extension we define the non-local operator square root in three type of bounded domains such as an interval, square or a ball. Also, as application we study the existence of weak solutions for a class of nonlinear elliptic problems.
topic	Harmonic extension Neumann boundary condition square root of the Laplacian nonlinear problem
url	http://ejde.math.txstate.edu/Volumes/2014/12/abstr.html
work_keys_str_mv	AT micheledeoliveiraalves anextensionproblemrelatedtothesquarerootofthelaplacianwithneumannboundarycondition AT sergiomunizoliva anextensionproblemrelatedtothesquarerootofthelaplacianwithneumannboundarycondition AT micheledeoliveiraalves extensionproblemrelatedtothesquarerootofthelaplacianwithneumannboundarycondition AT sergiomunizoliva extensionproblemrelatedtothesquarerootofthelaplacianwithneumannboundarycondition
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An extension problem related to the square root of the Laplacian with Neumann boundary condition

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