24,223 research outputs found
On Consistence of Material Coupling in a GL(3,R) Gauge Formulation of Gravity
A covariant scheme for material coupling with gauge formulation of
gravity is studied. We revisit a known idea of a Yang-Mills type construction,
where quadratical power of cosmological constant have to be considered in
consistence with vacuum Einstein's gravity. Then, matter coupling with gravity
is introduced and some constraints on fields and background appear. Finally,
exploring the N=3 case we elucidate that introduction of auxiliary fields
decreases the number of these constraints.Comment: 9 pages, LaTeX, title, and abstract changed. To appear in
Mod.Phys.Lett.A, Vol. 18, No. 25 (2003) pp. 1753-176
Multiple nonradial solutions for a nonlinear elliptic problem with singular and decaying radial potential
Many existence and nonexistence results are known for nonnegative radial
solutions to the equation with nonlinearites satisfying for some . Existence of
nonradial solutions, by contrast, is known only for , ,
and large enough. Here we show that the
equation has multiple nonradial solutions as for , , , and nonlinearities satisfying
suitable assumptions. Our argument essentially relies on the compact embeddings
between some suitable functional spaces of symmetric functions, which yields
the existence of nonnegative solutions of mountain-pass type, and the
separation of the corresponding mountain-pass levels from the energy levels
associated to radial solutions
An introduction to the study of critical points of solutions of elliptic and parabolic equations
We give a survey at an introductory level of old and recent results in the
study of critical points of solutions of elliptic and parabolic partial
differential equations. To keep the presentation simple, we mainly consider
four exemplary boundary value problems: the Dirichlet problem for the Laplace's
equation; the torsional creep problem; the case of Dirichlet eigenfunctions for
the Laplace's equation; the initial-boundary value problem for the heat
equation. We shall mostly address three issues: the estimation of the local
size of the critical set; the dependence of the number of critical points on
the boundary values and the geometry of the domain; the location of critical
points in the domain.Comment: 34 pages, 13 figures; a few slight changes and some references added;
to appear in the special issue, in honor of G. Alessandrini's 60th birthday,
of the Rendiconti dell'Istituto Matematico dell'Universit\`a di Triest
Consistence of a GL(3,R) gauge formulation for topological massive gravity
We include a Chern-Simons term in a GL(3,R) gauge formulation of gravity with
a cosmological contribution in 2+1 dimension and we explore consistence showing
that excitations must be causal and standard topological massive gravity is
recovered from this type of construction at the torsionless limit.Comment: Talk given at the Spanish Relativity Meeting 2007, Relativistic
Astrophysics and Cosmology, Puerto de la Cruz, Tenerife, Spai
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