384 research outputs found
The Ginzburg-Landau equation in the Heisenberg group
We consider a functional related with phase transition models in the
Heisenberg group framework. We prove that level sets of local minimizers
satisfy some density estimates, that is, they behave as "codimension one" sets.
We thus deduce a uniform convergence property of these level sets to interfaces
with minimal area.
These results are then applied in the construction of (quasi)periodic,
plane-like minimizers, i.e., minimizers of our functional whose level sets are
contained in a spacial slab of universal size in a prescribed direction. As a
limiting case, we obtain the existence of hypersurfaces contained in such a
slab which minimize the surface area with respect to a given periodic metric.Comment: 49 page
The Dirichlet problem for singular fully nonlinear operators
In this paper we prove existence of (viscosity) solutions of Dirichlet
problems concerning fully nonlinear elliptic operator, which are either
degenerate or singular when the gradient of the solution is zero. For this
class of operators it is possible to extend the concept of eigenvalue, this
paper concerns the cases when the inf of the principal eigenvalues is positive
i.e. when both the maximum and the minimum principle holds.Comment: 10 pages, 0 figure
A Neumann eigenvalue problem for fully nonlinear operators
In this paper we study the asymptotic behavior of the principal eigenvalues
associated to the Pucci operator in bounded domain with Neumann/Robin
boundary condition i.e. when tends to
infinity. This study requires Lipschitz estimates up to the boundary that are
interesting in their own rights.Comment: 19 page
Some Liouville Theorems for the p-Laplacian
We present several Liouville type results for the -Laplacian in .
Suppose that
is a nonnegative regular function such that We obtain the following
non -existence result:
1) Suppose that , and
is a nonnegative weak solution of - {\rm div} (|\nabla u|^{p-2 }\nabla u)
\geq h(x) u^q \;\;\mbox{in }\; \R^N . Suppose that then .
2) Let . If is a
weak solution bounded below of
in then is constant.
3) Let if is bounded from below and in then is constant.
4)If . If , then .Comment: 19 page
Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators
The main scope of this article is to define the concept of principal
eigenvalue for fully non linear second order operators in bounded domains that
are elliptic and homogenous. In particular we prove maximum and comparison
principle, Holder and Lipschitz regularity. This leads to the existence of a
first eigenvalue and eigenfunction and to the existence of solutions of
Dirichlet problems within this class of operators.Comment: 37 pages, 0 figure
Regularity for radial solutions of degenerate fully nonlinear equations
In this paper we prove Holder regularity of the derivative of radial
solutions to fully nonlinear equations when the operator is hessian, homogenous
of degree 1 in the Hessian, homogenous of some degree in the
gradient and which is elliptic when the gradient is not null.Comment: 20 page
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