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Asymptotics of the $s$-perimeter as $s\searrow 0$
Nonlinear problems nonlocal perimeter fractional Laplacian fractional Sobolev spaces minimal surfaces
2012/4/23
We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also p...
Approximation and relaxation of perimeter in the Wiener space
Approximation and relaxation of perimeter the Wiener space Analysis of PDEs
2011/9/13
Abstract: We characterize the relaxation of the perimeter in an infinite dimensional Wiener space, with respect to the weak L^2-topology. We also show that the rescaled Allen-Cahn functionals approxim...
Sets with High Volume and Low Perimeter
High Volume Low Perimeter Combinatorics Number Theory
2011/9/9
Abstract: In this paper, we consider a certain variation of the "isoperimetric problem" adopted for subsets of nonnegative integers. More specifically, we explore the sequence P(n) as described in OEI...
The Expected Perimeter in Eden and Related Growth Processes
Expected Perimeter Eden Related Growth Processes
2010/11/15
Following Richardson and using results of Kesten on First-passage percolation, we obtain an upper bound on the expected perimeter in an Eden Growth Process. Using results of the author from a problem...
A Note On the Accuracy of Ramanujan's Approximative Formula for the Perimeter of an Ellipse
Ramanujan's approximative formula Best constants Elliptic functions and integrals
2008/7/3
We present a detailed error analysis, with best possible constants, of Ramanujan's most accurate approximation to the perimeter of an ellipse.