Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Charles K. Smart"'
Publikováno v:
Communications on Pure and Applied Mathematics
We prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function, in the sense of approximation by polynomials with periodic corrections. Equivalently, the constants in the large-scale $C^{
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd113ee0a89c4dcd7942016ca2594eb8
http://hdl.handle.net/10138/353767
http://hdl.handle.net/10138/353767
Autor:
Charles K. Smart
Publikováno v:
IAS/Park City Mathematics Series. :131-154
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2560483cfe711e6ab4d3628f9c8eae28
https://doi.org/10.1090/pcms/027/04
https://doi.org/10.1090/pcms/027/04
Autor:
Charles K. Smart, Jeff Calder
Publikováno v:
Experts@Minnesota
Duke Math. J. 169, no. 11 (2020), 2079-2124
Duke Math. J. 169, no. 11 (2020), 2079-2124
We prove that the convex peeling of a random point set in dimension d approximates motion by the 1 / ( d + 1 ) power of Gaussian curvature. We use viscosity solution theory to interpret the limiting partial differential equation (PDE). We use the mar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08241fac464ef246857122f8386f7023
https://doi.org/10.1215/00127094-2020-0013
https://doi.org/10.1215/00127094-2020-0013
Autor:
Charles K. Smart, William M. Feldman
Publikováno v:
Archive for Rational Mechanics and Analysis. 232:389-435
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the limiting fre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50675f02e270c5952fc106c349e86470
https://doi.org/10.1007/s00205-018-1323-4
https://doi.org/10.1007/s00205-018-1323-4
View the abstract.
Autor:
Charles K. Smart, Scott N. Armstrong
Publikováno v:
Annales scientifiques de l'École normale supérieure. 49:423-481
Nous presentons des resultats quantitatifs pour l'homogeneisation de fonctionnelles integrales uniformement convexes avec coefficients aleatoires sous hypotheses d'independance. Le resultat principal est une estimation d'erreur pour le probleme de Di
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::25ee024e0ada36abd77530431e64a46d
https://doi.org/10.24033/asens.2287
https://doi.org/10.24033/asens.2287
Autor:
Jian Ding, Charles K. Smart
We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent on a large square is likely to decay exponentially.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67fecb4679d24d6c5d6d243d4e8f741c
http://arxiv.org/abs/1809.09041
http://arxiv.org/abs/1809.09041
Autor:
Charles K. Smart, Wesley Pegden
We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form elliptic equations. The stability results allows one to improve weak-* conver
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0bc998574bb8ebb141165bf82b62c33c
http://arxiv.org/abs/1708.09432
http://arxiv.org/abs/1708.09432
Publikováno v:
Annals of Mathematics. 186
We prove that the set of quadratic growths attainable by integer-valued superharmonic functions on the lattice $\mathbb{Z}^2$ has the structure of an Apollonian circle packing. This completely characterizes the PDE which determines the continuum scal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5f4582619d8e5e38cf214b67039993ad
https://doi.org/10.4007/annals.2017.186.1.1
https://doi.org/10.4007/annals.2017.186.1.1
We prove a result related to Bressan's mixing problem. We establish an inequality for the change of Bianchini semi-norms of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bi
Externí odkaz:
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http://arxiv.org/abs/1612.03431
http://arxiv.org/abs/1612.03431