Results 281 to 290 of about 128,747 (328)
Some of the next articles are maybe not open access.
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
openaire +1 more source
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
openaire +1 more source
On The Attainable Eigenvalues of the Laplace Operator
SIAM Journal on Mathematical Analysis, 1999Summary: 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
openaire +2 more sources
THE SPECTRUM OF THE 1-LAPLACE OPERATOR
Communications in Contemporary Mathematics, 2009The eigenfunction of the 1-Laplace operator is defined to be a critical point in the sense of the strong slope for a nonsmooth constraint variational problem. We completely write down all these eigenfunctions for the 1-Laplace operator on intervals.
openaire +1 more source
2017
We consider what is perhaps the most important of all partial differential operators, theLaplace operator (Laplacian) on \(\mathbb {R}^n\).
openaire +1 more source
We consider what is perhaps the most important of all partial differential operators, theLaplace operator (Laplacian) on \(\mathbb {R}^n\).
openaire +1 more source
MULTIPLE EIGENVALUES OF THE LAPLACE OPERATOR
Mathematics of the USSR-Sbornik, 1988The 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.
openaire +2 more sources
A nonholonomic Laplace operator
Journal of Soviet Mathematics, 1993See the review in Zbl 0779.53029.
Vershik, A. M., Gershkovich, V. Ya.
openaire +2 more sources
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
openaire +1 more source
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
openaire +1 more source
Strong Uniqueness for Laplace and Bi-Laplace Operators in the Limit Case
2001In this article we study some limiting cases of strong unique continuation for inequalities of the type $$ \left| {\Delta u\left( x \right)} \right| \leqslant \frac{A} {{\left| x \right|^2 }}\left| {u\left( x \right)} \right| + \frac{B} {{\left| x \right|}}\left| {\nabla u\left( x \right)} \right| x \in \Omega , $$ (1.1) or $$ \left ...
COLOMBINI, FERRUCCIO, GRAMMATICO C.
openaire +2 more sources
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 ...
openaire +1 more source
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 ...
openaire +1 more source