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The Higher Spin Laplace Operator [PDF]
Potential Analysis, 2015 This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group.
H. Bie, D. Eelbode, Matthias Roels
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Kompendium der reellen Analysis, 2019
In diesem Kapitel betrachten wir Differentialoperatoren, die in engem Zusammenhang mit der orthogonalen Gruppe der Raumdrehungen im \( {\mathbb{R}}^{n} \) stehen. Zum einen ist dies der sogenannte Laplace Operator \( \Delta = \sum\limits_{i = 1}^{n} {\partial_{i}^{2} } \) , gegeben durch die Summe der zweiten Ableitungen, und zum anderen der Euler ...
R. Weissauer
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In diesem Kapitel betrachten wir Differentialoperatoren, die in engem Zusammenhang mit der orthogonalen Gruppe der Raumdrehungen im \( {\mathbb{R}}^{n} \) stehen. Zum einen ist dies der sogenannte Laplace Operator \( \Delta = \sum\limits_{i = 1}^{n} {\partial_{i}^{2} } \) , gegeben durch die Summe der zweiten Ableitungen, und zum anderen der Euler ...
R. Weissauer
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Mathematical methods in the applied sciences, 2020
The paper deals with the following Kirchhoff‐type problem M∬ℝ2N1p(x,y)|v(x)−v(y)|p(x,y)|x−y|N+p(x,y)s(x,y)dxdy(−Δ)p(·)s(·)v(x)=μg(x,v)+|v|r(x)−2vinΩ,v=0inℝN\Ω, where M models a Kirchhoff coefficient, (−Δ)p(·)s(·) is a variable s(·)‐order p(·)‐fractional ...
J. Zuo, Tianqing An, A. Fiscella
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The paper deals with the following Kirchhoff‐type problem M∬ℝ2N1p(x,y)|v(x)−v(y)|p(x,y)|x−y|N+p(x,y)s(x,y)dxdy(−Δ)p(·)s(·)v(x)=μg(x,v)+|v|r(x)−2vinΩ,v=0inℝN\Ω, where M models a Kirchhoff coefficient, (−Δ)p(·)s(·) is a variable s(·)‐order p(·)‐fractional ...
J. Zuo, Tianqing An, A. Fiscella
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, 2017
We consider what is perhaps the most important of all partial differential operators, theLaplace operator (Laplacian) on \(\mathbb {R}^n\).
V. Serov
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We consider what is perhaps the most important of all partial differential operators, theLaplace operator (Laplacian) on \(\mathbb {R}^n\).
V. Serov
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ACM SIGGRAPH ASIA 2008 courses on - SIGGRAPH Asia '08, 2008
Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set of natural properties for discrete Laplace operators ...
Max Wardetzky +3 more
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Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set of natural properties for discrete Laplace operators ...
Max Wardetzky +3 more
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Extension technique for complete Bernstein functions of the Laplace operator
, 2017We discuss the representation of certain functions of the Laplace operator $$\Delta $$Δ as Dirichlet-to-Neumann maps for appropriate elliptic operators in half-space.
M. Kwaśnicki, J. Mucha
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2018
The fundamental properties of harmonic and subharmonic functions are given together with maximum principles, the representation of solutions of the Poisson equation, Weyl’s lemma and Perron’s method for proving existence of solutions of the Dirichlet problem.
David E. Edmunds, W. Desmond Evans
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The fundamental properties of harmonic and subharmonic functions are given together with maximum principles, the representation of solutions of the Poisson equation, Weyl’s lemma and Perron’s method for proving existence of solutions of the Dirichlet problem.
David E. Edmunds, W. Desmond Evans
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