107 research outputs found
The heart of a convex body
We investigate some basic properties of the {\it heart}
of a convex set It is a subset of
whose definition is based on mirror reflections of euclidean
space, and is a non-local object. The main motivation of our interest for
is that this gives an estimate of the location of the
hot spot in a convex heat conductor with boundary temperature grounded at zero.
Here, we investigate on the relation between and the
mirror symmetries of we show that
contains many (geometrically and phisically) relevant points of
we prove a simple geometrical lower estimate for the diameter of
we also prove an upper estimate for the area of
when is a triangle.Comment: 15 pages, 3 figures. appears as "Geometric Properties for Parabolic
and Elliptic PDE's", Springer INdAM Series Volume 2, 2013, pp 49-6
Second-order -regularity in nonlinear elliptic problems
A second-order regularity theory is developed for solutions to a class of
quasilinear elliptic equations in divergence form, including the -Laplace
equation, with merely square-integrable right-hand side. Our results amount to
the existence and square integrability of the weak derivatives of the nonlinear
expression of the gradient under the divergence operator. This provides a
nonlinear counterpart of the classical -coercivity theory for linear
problems, which is missing in the existing literature. Both local and global
estimates are established. The latter apply to solutions to either Dirichlet or
Neumann boundary value problems. Minimal regularity on the boundary of the
domain is required. If the domain is convex, no regularity of its boundary is
needed at all
On the regularity up to the boundary for certain nonlinear elliptic systems
We consider a class of nonlinear elliptic systems and we prove regularity up to the boundary for second order derivatives. In the proof we trace carefully the dependence on the various parameters of the problem, in order to establish, in a further work, results for more general systems
Twenty years of coordination technologies: State-of-the-art and perspectives
Since complexity of inter- and intra-systems interactions is steadily increasing in modern application scenarios (e.g., the IoT), coordination technologies are required to take a crucial step towards maturity. In this paper we look back at the history of the COORDINATION conference in order to shed light on the current status of the coordination technologies there proposed throughout the years, in an attempt to understand success stories, limitations, and possibly reveal the gap between actual technologies, theoretical models, and novel application needs
Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science): Preface
Spray computers: Frontiers of self-organization
The two different approaches to self-organization in spray-computers are discussed. Direct engineering approaches to self-organization aim at defining distributed algorithm to lead a system to a final coherent global state. The method enables engineers to achieve a specific robust self-organized behavior. The reverse engineering approaches to self-configuration aim at achieving complex coordinated behaviors in spray computers by recreating the conditions enabling complex coordinated behaviors. The approach allows to rely on the results from other disciplines to explore a variety of complex coordiantion phenomena to be exploited in spary computers
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