1,156 research outputs found
regularity of solutions of degenerate fully non-linear elliptic equations
In the present paper, a class of fully non-linear elliptic equations are
considered, which are degenerate as the gradient becomes small. H\"older
estimates obtained by the first author (2011) are combined with new Lipschitz
estimates obtained through the Ishii-Lions method in order to get
estimates for solutions of these equations.Comment: Submitte
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
Symmetry minimizes the principal eigenvalue: an example for the Pucci's sup operator
We explicitly evaluate the principal eigenvalue of the extremal Pucci's
sup--operator for a class of special plane domains, and we prove that, for
fixed area, the eigenvalue is minimal for the most symmetric set.Comment: 11 pages, 7 figure
Symmetry for solutions of two-phase semilinear elliptic equations on hyperbolic space
Assume that where is a double-well potential. Under
certain conditions on the Lipschitz constant of on , we prove that
arbitrary bounded global solutions of the semilinear equation
on hyperbolic space \HH^n must reduce to functions of one variable provided
they admit asymptotic boundary values on the infinite boundary of \HH^n which
are invariant under a cohomogeneity one subgroup of the group of isometries of
\HH^n. We also prove existence of these one-dimensional solutions.Comment: 24 page
Eigenfunctions for singular fully non linear equations in unbounded domains
In this paper we prove some Harnack inequality for fully non linear
degenerate elliptic equations, in the two dimensional case, extending the
results of Davila Felmer and Quaas in the singular case but in all dimensions.
We then apply this result for the existence of an eigenfunction in smooth
bounded domain.Comment: 30 pages 2 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
The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity
We investigate the homogeneous Dirichlet problem in uniformly convex domains
for a large class of degenerate elliptic equations with singular zero order
term. In particular we establish sharp existence and uniqueness results of
positive viscosity solutions.Comment: 13 page
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