The Experts below are selected from a list of 90 Experts worldwide ranked by ideXlab platform
Mukund Madhav Mishra - One of the best experts on this subject based on the ideXlab platform.
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The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group ℍ
Potential Analysis, 2016Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Korányi ball on the Heisenberg group ℍ n $\mathbb {H}_{n}$ are discussed. Explicit representation for a Green’s type Function (Neumann Function) for the Korányi ball in ℍ n $\mathbb {H}_{n}$ for circular Functions has been obtained. This Function is then used on the above region in ℍ n $\mathbb {H}_{n}$ to solve the inhomogeneous Neumann boundary value problem for certain circular data.
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The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group \(\mathbb H_{n}\)
Potential Analysis, 2016Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Koranyi ball on the Heisenberg group \(\mathbb {H}_{n}\) are discussed. Explicit representation for a Green’s type Function (Neumann Function) for the Koranyi ball in \(\mathbb {H}_{n}\) for circular Functions has been obtained. This Function is then used on the above region in \(\mathbb {H}_{n}\) to solve the inhomogeneous Neumann boundary value problem for certain circular data.
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Neumann boundary value problem in domains of the Heisenberg Group $\mathbb H_n$
arXiv: Analysis of PDEs, 2014Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:Existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian on the Kor\'anyi ball of the Heisenberg group $\mathbb{H}_n$ are discussed. Explicit representations of Green's type Function (Neumann Function) for the half space and Kor\'anyi ball in $\mathbb{H}_n$ for circular Functions have been obtained. These Functions are then used on above regions in $\mathbb{H}_n$ to solve the inhomogeneous Neumann boundary value problem for circular data.
Shivani Dubey - One of the best experts on this subject based on the ideXlab platform.
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The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group ℍ
Potential Analysis, 2016Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Korányi ball on the Heisenberg group ℍ n $\mathbb {H}_{n}$ are discussed. Explicit representation for a Green’s type Function (Neumann Function) for the Korányi ball in ℍ n $\mathbb {H}_{n}$ for circular Functions has been obtained. This Function is then used on the above region in ℍ n $\mathbb {H}_{n}$ to solve the inhomogeneous Neumann boundary value problem for certain circular data.
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The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group \(\mathbb H_{n}\)
Potential Analysis, 2016Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Koranyi ball on the Heisenberg group \(\mathbb {H}_{n}\) are discussed. Explicit representation for a Green’s type Function (Neumann Function) for the Koranyi ball in \(\mathbb {H}_{n}\) for circular Functions has been obtained. This Function is then used on the above region in \(\mathbb {H}_{n}\) to solve the inhomogeneous Neumann boundary value problem for certain circular data.
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Neumann boundary value problem in domains of the Heisenberg Group $\mathbb H_n$
arXiv: Analysis of PDEs, 2014Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:Existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian on the Kor\'anyi ball of the Heisenberg group $\mathbb{H}_n$ are discussed. Explicit representations of Green's type Function (Neumann Function) for the half space and Kor\'anyi ball in $\mathbb{H}_n$ for circular Functions have been obtained. These Functions are then used on above regions in $\mathbb{H}_n$ to solve the inhomogeneous Neumann boundary value problem for circular data.
Ajay Kumar - One of the best experts on this subject based on the ideXlab platform.
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The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group ℍ
Potential Analysis, 2016Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Korányi ball on the Heisenberg group ℍ n $\mathbb {H}_{n}$ are discussed. Explicit representation for a Green’s type Function (Neumann Function) for the Korányi ball in ℍ n $\mathbb {H}_{n}$ for circular Functions has been obtained. This Function is then used on the above region in ℍ n $\mathbb {H}_{n}$ to solve the inhomogeneous Neumann boundary value problem for certain circular data.
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The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group \(\mathbb H_{n}\)
Potential Analysis, 2016Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Koranyi ball on the Heisenberg group \(\mathbb {H}_{n}\) are discussed. Explicit representation for a Green’s type Function (Neumann Function) for the Koranyi ball in \(\mathbb {H}_{n}\) for circular Functions has been obtained. This Function is then used on the above region in \(\mathbb {H}_{n}\) to solve the inhomogeneous Neumann boundary value problem for certain circular data.
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Neumann boundary value problem in domains of the Heisenberg Group $\mathbb H_n$
arXiv: Analysis of PDEs, 2014Co-Authors: Shivani Dubey, Ajay Kumar, Mukund Madhav MishraAbstract:Existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian on the Kor\'anyi ball of the Heisenberg group $\mathbb{H}_n$ are discussed. Explicit representations of Green's type Function (Neumann Function) for the half space and Kor\'anyi ball in $\mathbb{H}_n$ for circular Functions have been obtained. These Functions are then used on above regions in $\mathbb{H}_n$ to solve the inhomogeneous Neumann boundary value problem for circular data.
Shaozhong Deng - One of the best experts on this subject based on the ideXlab platform.
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Comment on “On the Neumann Function and the method of images in spherical and ellipsoidal geometry”
Mathematical Methods in the Applied Sciences, 2017Co-Authors: Changfeng Xue, Shaozhong DengAbstract:In this note, we point out two errors in the article “On the Neumann Function and the method of images in spherical and ellipsoidal geometry” by Dassios and Sten. Two corrections are then proposed.
Johan C.-e. Sten - One of the best experts on this subject based on the ideXlab platform.
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On the Neumann Function and the method of images in spherical and ellipsoidal geometry
Mathematical Methods in the Applied Sciences, 2012Co-Authors: George Dassios, Johan C.-e. StenAbstract:The invention of an image system for a boundary value problem adds to a significant understanding of the structure of the problem, both at the mathematical and at the physical level. In this paper, the interior and exterior Neumann Functions for the Laplacian in the cases of spherical and ellipsoidal domains are represented in terms of images. Besides isolated images, the presence of the normal derivative in the Neumann condition demands an additional continuous distribution of images, which in the spherical cases, can be restricted to a one-dimensional manifold, whereas for the ellipsoid, both a one-dimensional and a two-dimensional distribution of images is needed. Copyright © 2012 John Wiley & Sons, Ltd.
