2,412 research outputs found
2019 CIME summer school Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems
No full textThis volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing an up-to-date account of the Yau conjecture, a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves, it will be of interest to students and researchers in mathematical analysis and its applications
Homogenization of the Neumann problem in perforated domains: an alternative approach
No full textThe main result of this paper is a compactness theorem for families of functions in the space SBV (Special functions of Bounded Variation)
defined on periodically perforated domains P. Our analysis avoids the use of any extension procedure in SBV , weakens
the hypotheses on P to the minimal one
Static Analysis of Authentication
No full textAuthentication protocols are very simple distributed algorithms whose purpose is to enable two entities to achieve mutual and reliable agreement on some piece of information, typically the identity of the other party, its presence, the origin of a message, its intended destination. Achieving the intended agreement guarantees is subtle because they typically are the result of the encryption/decryption of messages composed of different parts, with each part providing a “piece” of the authentication guarantee. This tutorial paper presents the basics of authentication protocols and illustrates a specific technique for statically analysing protocol specifications. The technique allows us to validate protocols in the presence of both malicious outsiders and compromised insiders, with no limitation on the number of parallel sessions.
This paper covers the course “Static Analysis of Authentication” given by the author at the FOSAD’04 school. The static analysis technique described here is a joint work with Michele Bugliesi and Matteo Maffei (Università di Venezia
Match It or Die: Proving Integrity by Equality
No full textCryptographic hash functions are commonly used as modification detection codes. The goal is to provide message integrity assurance by comparing the digest of the original message with the hash of what is thought to be the intended message. This paper generalizes this idea by applying it to general expressions instead of just digests: success of an equality test between a tainted data and a trusted one can be seen as a proof of high-integrity for the first item. Secure usage of hash functions is also studied with respect to the confidentiality of digests by extending secret-sensitive noninterference of Demange and Sands
Types for security protocols
No full textWe revise existing type-based analyses of security protocols by devising core type system for secrecy, integrity and authentication in the setting of spi-calculus processes. These fundamental security properties are usually studied independently. Our exercise of considering all of them in a uniform framework is interesting under different perspectives: (i) it provides a general overview of how type theory can be applied to reason on security protocols; (ii) it illustrates and compares the main results and techniques in literature; (iii) perhaps more importantly, it shows that by combining techniques deployed for different properties, existing type-systems can be significantly simplified
An epiperimetric inequality for the thin obstacle problem
No full textWe prove an epiperimetric inequality for the thin obstacle problem, extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study the rate of converge of the rescaled solutions to their limits, as well as the regularity properties of the free boundary
An intrinsic approach to manifold constrained variational problems
No full textMotivated by some questions in continuum mechanics and analysis in metric spaces, we give an intrinsic characterization of sequentially weak lower semicontinuous functionals defined on Sobolev maps with values into manifolds without embedding the target into Euclidean spaces
On the measure and the structure of the free boundary of the Lower dimensional obstacle problem
No full textWe provide a thorough description of the free boundary for the lower dimensional obstacle problem in R^{n+1} up to sets of null H^{n−1} measure. In particular, we prove (i) local finiteness of the (n−1)-dimensional Hausdorff measure of the free boundary, (ii) H^{n−1}-rectifiability of the free boundary, (iii) classification of the frequencies up to a set of dimension at most (n-2) and classification of the blow-ups at H^{n−1} almost every free boundary point
Monotonicity formulas for obstacle problems with Lipschitz coefficients
No full textWe prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a Hölder continuous linear term. With the help of those formulas we are able to carry out the full analysis of the regularity of free-boundary points following the approaches by Caffarelli, Weiss and Monneau
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