Problem of compatibility and orthogonal decomposition of second-order symmetric tensors in a compact Riemannian manifold with boundary

1977 ◽  
Vol 64 (3) ◽  
pp. 221-243 ◽  
Author(s):  
Tsuan Wu Ting
Keyword(s):  
Riemannian Manifold ◽  
Compact Riemannian Manifold ◽  
Second Order ◽  
Orthogonal Decomposition ◽  
Symmetric Tensors ◽  
Manifold With Boundary

scholarly journals Second-Order Elliptic Equation with Singularities

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Hichem Boughazi
Keyword(s):  
Riemannian Manifold ◽  
Elliptic Equation ◽  
Compact Riemannian Manifold ◽  
Second Order ◽  
Singular Equation ◽  
Order Elliptic Equation ◽  
Nontrivial Solutions ◽  
Geometric Application ◽  
Second Order Elliptic Equation

On the compact Riemannian manifold of dimension n≥5, we study the existence and regularity of nontrivial solutions for nonlinear second-order elliptic equation with singularities. At the end, we give a geometric application of the above singular equation.

scholarly journals Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary

2017 ◽  
Vol 8 (1) ◽  
pp. 559-582 ◽  
Author(s):  
Mónica Clapp ◽  
Marco Ghimenti ◽  
Anna Maria Micheletti
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Compact Riemannian Manifold ◽  
Semiclassical Limit ◽  
Arbitrary Dimension ◽  
Neumann Boundary ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Manifold With Boundary ◽  
Klein Gordon

Abstract We study the semiclassical limit to a singularly perturbed nonlinear Klein–Gordon–Maxwell–Proca system, with Neumann boundary conditions, on a Riemannian manifold {\mathfrak{M}} with boundary. We exhibit examples of manifolds, of arbitrary dimension, on which these systems have a solution which concentrates at a closed submanifold of the boundary of {\mathfrak{M}} , forming a positive layer, as the singular perturbation parameter goes to zero. Our results allow supercritical nonlinearities and apply, in particular, to bounded domains in {\mathbb{R}^{N}} . Similar results are obtained for the more classical electrostatic Klein–Gordon–Maxwell system with appropriate boundary conditions.

scholarly journals Study of a second-order nonlinear elliptic problem generated by a divergence type operator on a compact Riemannian manifold

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4811-4820
Author(s):  
A. Abnoune ◽  
E. Azroul ◽  
M.T.K. Abbassi
Keyword(s):  
Riemannian Manifold ◽  
Elliptic Problem ◽  
Compact Riemannian Manifold ◽  
Second Order ◽  
Type Operator ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic ◽  
Divergence Type

In this paper, we will study a second-order nonlinear elliptic problem generated by an operator of divergence type (or type leray-Lion) : (P1){ A(u) = f in M u = 0 on ? (1) on (M,g) a compact Riemannian manifold et ? its border.

EXTREMAL FUNCTIONS FOR MOSER–TRUDINGER INEQUALITIES ON 2-DIMENSIONAL COMPACT RIEMANNIAN MANIFOLDS WITH BOUNDARY

2006 ◽  
Vol 17 (03) ◽  
pp. 313-330 ◽  
Author(s):  
YUNYAN YANG
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Compact Riemannian Manifold ◽  
Extremal Functions ◽  
Manifolds With Boundary ◽  
Manifold With Boundary ◽  
Blowing Up

Let (M,g) be a 2-dimensional compact Riemannian manifold with boundary. In this paper, we use the method of blowing up analysis to prove the existence of the extremal functions for some Moser–Trudinger inequalities on (M,g).

scholarly journals Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Function ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Smooth Functions ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.

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