Results 181 to 190 of about 8,080 (219)

A nonholonomic Laplace operator [PDF]

open access: possibleJournal of Soviet Mathematics, 1993
See the review in Zbl 0779.53029.
Anatoly Vershik, V. Ya. Gershkovich
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On The Attainable Eigenvalues of the Laplace Operator

SIAM Journal on Mathematical Analysis, 1999
Summary: We consider the subset \(E\) of \(\mathbb{R}^2\) of all points whose first and second components, respectively, coincide with the first and second eigenvalues of the Laplace operator \(-\Delta\) with zero boundary conditions on domains of \(\mathbb{R}^N\) with prescribed measure. We show that the set \(E\) is closed in \(\mathbb{R}^2\).
D. Bucur   +2 more
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The Laplace Operator

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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MULTIPLE EIGENVALUES OF THE LAPLACE OPERATOR [PDF]

open access: possibleMathematics of the USSR-Sbornik, 1988
The estimates from above for the multiplicity of the eigenvalues of the Schrödinger operators on compact Riemannian two-dimensional manifolds are obtained. The paper contains also several examples illustrating the sharpness of the results.
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The Laplace Operator

2017
We consider what is perhaps the most important of all partial differential operators, theLaplace operator (Laplacian) on \(\mathbb {R}^n\).
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Der Laplace Operator

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 ...
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