364 research outputs found
Entropy-based measure of structural order in water
We analyze the nature of the structural order established in liquid TIP4P
water in the framework provided by the multi-particle correlation expansion of
the statistical entropy. Different regimes are mapped onto the phase diagram of
the model upon resolving the pair entropy into its translational and
orientational components. These parameters are used to quantify the relative
amounts of positional and angular order in a given thermodynamic state, thus
allowing a structurally unbiased definition of low-density and high-density
water. As a result, the structurally anomalous region within which both types
of order are simultaneously disrupted by an increase of pressure at constant
temperature is clearly identified through extensive molecular-dynamics
simulations.Comment: 5 pages, 2 figures, to appear in Phys. Rev. E (Rapid Communication
Geometric approach to nonvariational singular elliptic equations
In this work we develop a systematic geometric approach to study fully
nonlinear elliptic equations with singular absorption terms as well as their
related free boundary problems. The magnitude of the singularity is measured by
a negative parameter , for , which reflects on
lack of smoothness for an existing solution along the singular interface
between its positive and zero phases. We establish existence as well sharp
regularity properties of solutions. We further prove that minimal solutions are
non-degenerate and obtain fine geometric-measure properties of the free
boundary . In particular we show sharp
Hausdorff estimates which imply local finiteness of the perimeter of the region
and a.e. weak differentiability property of
.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos
Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis
201
Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth
We establish global regularity for weak solutions to quasilinear divergence
form elliptic and parabolic equations over Lipschitz domains with controlled
growth conditions on low order terms. The leading coefficients belong to the
class of BMO functions with small mean oscillations with respect to .Comment: 24 pages, to be submitte
On the symmetry of minimizers
For a large class of variational problems we prove that minimizers are
symmetric whenever they are .Comment: 17 pages, to appear in Arch. Rational Mech. Anal.; added Example 7
and some reference
Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
The main result of this paper concerns the behavior of a free boundary
arising from a minimization problem, close to the fixed boundary in two
dimensions
Non-uniqueness in conformal formulations of the Einstein constraints
Standard methods in non-linear analysis are used to show that there exists a
parabolic branching of solutions of the Lichnerowicz-York equation with an
unscaled source. We also apply these methods to the extended conformal thin
sandwich formulation and show that if the linearised system develops a kernel
solution for sufficiently large initial data then we obtain parabolic solution
curves for the conformal factor, lapse and shift identical to those found
numerically by Pfeiffer and York. The implications of these results for
constrained evolutions are discussed.Comment: Arguments clarified and typos corrected. Matches published versio
Boundary regularity for the Poisson equation in reifenberg-flat domains
This paper is devoted to the investigation of the boundary regularity for the
Poisson equation {{cc} -\Delta u = f & \text{in} \Omega u= 0 & \text{on}
\partial \Omega where belongs to some and is a
Reifenberg-flat domain of More precisely, we prove that given an
exponent , there exists an such that the
solution to the previous system is locally H\"older continuous provided
that is -Reifenberg-flat. The proof is based on
Alt-Caffarelli-Friedman's monotonicity formula and Morrey-Campanato theorem
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