Results 21 to 30 of about 534 (49)

Elliptic operators and their symbols

Demonstratio Mathematica, 2019
We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs a Fredholm ...
Vasilyev Vladimir
doaj   +1 more source

Heat flow method to Lichnerowicz type equation on closed manifolds

, 2010
In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\geq0$ are given smooth ...
D.H. Sattinger, E. Hebey, J. Isenberg, L. Ma, Li Ma, O. Druet, Th. Aubin, Xiao Tang, Y. Choquet-Bruhat, Y. Choquet-Bruhat, Y. Du, Yuhua Sun   +11 more
core   +1 more source

Lichnerowicz-type equations on complete manifolds

Advances in Nonlinear Analysis, 2016
Under appropriate spectral assumptions, we prove two existence results for positive solutions of Lichnerowicz-type equations on complete manifolds.
Albanese Guglielmo, Rigoli Marco
doaj   +1 more source

Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators

, 2006
We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a ...
Campos R. G., Campos R. G., Campos R. G., Friedrich T., Graf W., J. L. LÓPEZ-LÓPEZ, R. VERA, RAFAEL G. CAMPOS, Trautman A.   +8 more
core   +1 more source

New multiplicity results in prescribing Q-curvature on standard spheres

Advanced Nonlinear Studies
In this paper, we study the problem of prescribing Q-Curvature on higher dimensional standard spheres. The problem consists in finding the right assumptions on a function K so that it is the Q-Curvature of a metric conformal to the standard one on the ...
Ben Ayed Mohamed, El Mehdi Khalil
doaj   +1 more source

Examples of non-isolated blow-up for perturbations of the scalar curvature equation on non locally conformally flat manifolds [PDF]

, 2014
Solutions to scalar curvature equations have the property that all possible blow-up points are isolated, at least in low dimensions. This property is commonly used as the first step in the proofs of compactness. We show that this result becomes false for
Robert, Frédéric, Vétois, Jérôme
core   +2 more sources

Matrix Inequality for the Laplace Equation

, 2017
Since Li and Yau obtained the gradient estimate for the heat equation, related estimates have been extensively studied. With additional curvature assumptions, matrix estimates that generalize such estimates have been discovered for various time-dependent
Park, Jiewon
core   +1 more source

On subsolutions and concavity for fully nonlinear elliptic equations

Advanced Nonlinear Studies
Subsolutions and concavity play critical roles in classical solvability, especially a priori estimates, of fully nonlinear elliptic equations. Our first primary goal in this paper is to explore the possibility to weaken the concavity condition.
Guan Bo
doaj   +1 more source

An energy gap for Yang-Mills connections

, 2009
Consider a Yang-Mills connection over a Riemann manifold $M=M^n$, $n\ge 3$, where $M$ may be compact or complete. Then its energy must be bounded from below by some positive constant, if $M$ satisfies certain conditions, unless the connection is flat ...
Gerhardt, Claus
core   +1 more source

Estimates for the volume of a Lorentzian manifold

, 2002
We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume.Comment: 8 pages, a pdf version of the preprint can also be retrieved from http://www.math ...
C. Gerhardt, C. Gerhardt, C. Gerhardt, Claus Gerhardt, D. Eardley, S. W. Hawking   +5 more
core   +3 more sources