Results 21 to 30 of about 211,213 (315)

Nonlinear boundary value problems involving the extrinsic mean curvature operator [PDF]

Mathematica Bohemica, 2014
Summary: The paper surveys recent results obtained for the existence and multiplicity of radial solutions of Dirichlet problems of the type \[ \nabla \cdot \bigg (\frac {\nabla v}{\sqrt {1 - | \nabla v| ^2}}\bigg) = f(| x| ,v) \quad \text{in} \;B_R,\quad u = 0 \quad \text{on} \;\partial B_R , \] where \(B_R\) is the open ball of center \(0\) and radius
Jean Mawhin
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Scalar and mean curvature comparison via the Dirac operator

Geometry & Topology, 2021
We use the Dirac operator technique to establish sharp distance estimates for compact spin manifolds under lower bounds on the scalar curvature in the interior and on the mean curvature of the boundary. In the situations we consider, we thereby give refined answers to questions on metric inequalities recently proposed by Gromov.
S. Cecchini, Rudolf Zeidler
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Second Eigenvalue of Paneitz Operators and Mean Curvature [PDF]

Communications in Mathematical Physics, 2011
For $n\geq 7$, we give the optimal estimate for the second eigenvalue of Paneitz operators for compact $n$-dimensional submanifolds in an $(n+p)$-dimensional space form.
Daguang Chen, Haizhong Li
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A note on parallel mean curvature surfaces and Codazzi operators [PDF]

Archiv der Mathematik, 2023
We present an intrinsic Klotz-Osserman type theorem for surfaces in terms of Codazzi operators. Additionally, utilizing Simons' formula, we investigate surfaces with parallel mean curvature with non-positive Gaussian curvature in product spaces.
Felippe Guimarães
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Positive radial solutions for systems with mean curvature operator in Minkowski space

, 2017
We are concerned with a Dirichlet system, involving the mean curvature operator in Minkowski space M(w) = div (∇w / 1−|∇w|2) in a ball in RN. Using topological degree arguments, critical point theory and lower and upper solutions method, we obtain non existence, existence and multiplicity of radial, positive solutions.
Daniela Gurban, Petru Jebelean
semanticscholar   +5 more sources

Problems with mean curvature-like operators and three-point boundary conditions [PDF]

Bulletin of the Brazilian Mathematical Society, New Series, 2016
14 pages.
Dionicio Pastor Dallos Santos
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One-signed rotationally symmetric solutions of singular Dirichlet problems with the prescribed higher mean curvature operator in Minkowski spacetime

Mathematical Modelling and Analysis
We investigate the existence, uniqueness and multiplicity of one-signed rotationally symmetric solutions of singular Dirichlet problems with the prescribed higher mean curvature operator in Minkowski spacetime. The main tools are the Schauder fixed point
Meiyu Liu, Minghe Pei, Libo Wang
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Saddle solutions for Allen-Cahn type equations involving the prescribed mean curvature operator [PDF]

Milan Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Renan J. S. Isneri
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Non-potential and non-radial Dirichlet systems with mean curvature operator in Minkowski space

Discrete and Continuous Dynamical Systems. Series A, 2019
We deal with a multiparameter Dirichlet system having the form \begin{document}$ \begin{equation*} \left\{ \begin{array}{ll} -\mathcal M(u) = \lambda_1f_1(u,v), & \hbox{in $\Omega$},\\ -\mathcal M(v) = \lambda_2f_2(u,v), & \hbox{in $\Omega$},\\ u|_ ...
Daniela Gurban, Petru Jebelean, Călin Şerban   +2 more
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On the 𝐿ᵣ-operators penalized by (𝑟+1)-mean curvature [PDF]

Proceedings of the American Mathematical Society, 2018
In this paper, we establish the non-positivity of the second eigenvalue of the Schrödinger operator − div ( P r ∇ ⋅ ) − W r 2 -\textrm ...
Leo Souza
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