AN EXTENSION PROBLEM RELATED TO THE SQUARE ROOT OF THE LAPLACIAN WITH NEUMANN BOUNDARY CONDITION

被引：0

作者：

Alves, Michele De Oliveira ^{[1
]}

Oliva, Sergio Muniz ^{[2
]}

机构：

[1] Univ Estadual Londrina, Dept Matemat, Londrina, Brazil

[2] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Sao Paulo, Brazil

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年

关键词：

Harmonic extension; Neumann boundary condition; square root of the Laplacian; nonlinear problem;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：18

共 50 条

[1] The Nehari manifold approach for p(x)-Laplacian problem with Neumann boundary condition
Taghavi, A.
Afrouzi, G. A.
Ghorbani, H.
[J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2013, (39) : 1 - 14
[2] THE PRINCIPAL EIGENVALUE OF THE ∞-LAPLACIAN WITH THE NEUMANN BOUNDARY CONDITION
Patrizi, Stefania
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2011, 17 (02) : 575 - 601
[3] THE ANISOTROPIC ∞-LAPLACIAN EIGENVALUE PROBLEM WITH NEUMANN BOUNDARY CONDITIONS
Piscitelli, Gianpaolo
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2019, 32 (11-12) : 705 - 734
[4] The Neumann problem for the fractional Laplacian: regularity up to the boundary
Audrito, Alessandro
Felipe-Navarro, Juan-Carlos
Ros-Oton, Xavier
[J]. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2023, 24 (02) : 1155 - 1222
[5] On the lowest eigenvalue of the Laplacian with Neumann boundary condition at a small obstacle
Hempel, R
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 194 (01) : 54 - 74
[6] Existence of Solutions for the Laplacian Equation with Exponential Neumann Boundary Condition
Tao Zhang
Changliang Zhou
Chunqin Zhou
[J]. Frontiers of Mathematics, 2023, 18 : 797 - 816
[7] Existence of Solutions for the Laplacian Equation with Exponential Neumann Boundary Condition
Zhang, Tao
Zhou, Changliang
Zhou, Chunqin
[J]. FRONTIERS OF MATHEMATICS, 2023, 18 (04): : 797 - 816
[8] Feature generation using the Laplacian operator with Neumann boundary condition
Khabou, Mohamed A.
Rhouma, Mohamed B. H.
Hermi, Lotfi
[J]. PROCEEDINGS IEEE SOUTHEASTCON 2007, VOLS 1 AND 2, 2007, : 766 - +
[9] An extension problem related to the fractional Laplacian
Caffarelli, Luis
Silvestre, Luis
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1245 - 1260
[10] Eigenvalues for a Neumann Boundary Problem Involving the P(x)-Laplacian
Miao, Qing
[J]. ADVANCES IN MATHEMATICAL PHYSICS, 2015, 2015

← 1 2 3 4 5 →