In this paper, we derive the evolution equation for the first eigenvalue of Laplace operator along powers of mean curvature flow. Considering a compact, strictly convex n-dimensional surface M without boundary, which is smoothly immersed in ℝ n+1, we prove that if the initial 2-dimensional...
Laplace-type operatorfirst eigenvaluecharacterization of hyperellipsoidsAccording to Tashiro–Obata, on a Riemannian manifold ( M , g ) with its Ricci curvature bounded positively from below, the first eigenvalue of the Laplacian on functions satisfies a simple inequality in terms of the scalar ...
Prashanth, Simplicity of principal eigenvalue for p-Laplace operator with singular weight, Arch. Math., 86 (2006), 79-89. 26Lucia M. and Prashant S., Simplicity of principal eigenvalue for p-Laplace operator with sin- gular indefinite weight, Archiv der Math. 86 (2006), 79-89....
DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM. We consider a number of problems that are associated with the 1-Laplace operator Div (Du/|Du|), the formal limit of the p-Laplace operator for p → 1, by i... KAWOHL,BERND,SCHURICHT,... - 《Communications...
摘要: Let (,g) be an -dimensional closed Riemannian manifold with the Ricci curvature bounded from below. In the present paper we get the lower bound of the first eigenvalue of the -Laplace operator, which generalizes the results of Lichnerowicz and Yang Hong-cang.关键词:...
Abstract We study nonlinear eigenvalue problems for the p -Laplace operator subject to different kinds of boundary conditions on a bounded domain. Using the Ljusternik–Schnirelman principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues. We prove the simplicity and iso...
Let (M,g) be an n-dimensional closed Riemannian manifold with the Ricci curvature bounded from below. In the present paper we get the lower bound of the fi
and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. ...
in the sense of Chung and Yau is proved to be a graph with Ricci curvature bounded below by zero. We also get an estimate for the eigenvalue of Laplace operator on finite graphs: lambda >= 1/dD(exp(dD 1) - 1), where d is the weighted degree of G, and D is the diameter of ...
Kellogg, Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical ... H Walden,RB Kellogg - 《Journal of Engineering Mathematics》 被引量: 58发表: 1977年 Numerical modelling of the galvanic coupling in aluminium alloys: A discussion on the application of local...