Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Scott N. Armstrong"'
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
Publikováno v:
Communications on Pure and Applied Mathematics
We consider nonlinear, uniformly elliptic equations with random, highly oscillating coefficients satisfying a finite range of dependence. We prove that homogenization and linearization commute in the sense that the linearized equation (linearized aro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e97883f7b7f30ec0269d839413a856ab
https://doi.org/10.1002/cpa.21902
https://doi.org/10.1002/cpa.21902
Publikováno v:
ESAIM: Mathematical Modelling and Numerical Analysis
ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (1), pp.37-55. ⟨10.1051/m2an/2020080⟩
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2021, 55 (1), pp.37-55. ⟨10.1051/m2an/2020080⟩
ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (1), pp.37-55. ⟨10.1051/m2an/2020080⟩
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2021, 55 (1), pp.37-55. ⟨10.1051/m2an/2020080⟩
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address different len
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30e731e728a8dc87bef24765e9dec4df
https://aaltodoc.aalto.fi/handle/123456789/103284
https://aaltodoc.aalto.fi/handle/123456789/103284
Autor:
Sylvia Serfaty, Scott N. Armstrong
Publikováno v:
Ann. Probab. 49, no. 1 (2021), 46-121
We study Coulomb gases in any dimension $d \geq 2$ and in a broad temperature regime. We prove local laws on the energy, separation and number of points down to the microscopic scale. These yield the existence of limiting point processes generalizing
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::026591b608a0cdd6f30b262d20383f85
https://doi.org/10.1214/20-aop1445
https://doi.org/10.1214/20-aop1445
Publikováno v:
Archive for Rational Mechanics and Analysis
We prove large-scale $C^\infty$ regularity for solutions of nonlinear elliptic equations with random coefficients, thereby obtaining a version of the statement of Hilbert's 19th problem in the context of homogenization. The analysis proceeds by itera
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c784e49d338a51df54563d36c7799091
Publikováno v:
Journal of the European Mathematical Society
Journal of the European Mathematical Society, European Mathematical Society, 2018, 20 (4), pp.797-864. ⟨10.4171/JEMS/777⟩
Journal of the European Mathematical Society, European Mathematical Society, 2018, 20 (4), pp.797-864. ⟨10.4171/JEMS/777⟩
International audience; We study random homogenization of second-order, degenerate and quasilinear Hamilton-Jacobi equations which are positively homogeneous in the gradient. Included are the equations of forced mean curvature motion and others descr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78fa80c9932fa9edaafd87b5e918aec0
https://doi.org/10.4171/jems/777
https://doi.org/10.4171/jems/777
Autor:
Paul Dario, Scott N. Armstrong
Publikováno v:
Communications on Pure and Applied Mathematics. 71:1717-1849
We establish quantitative homogenization, large-scale regularity and Liouville results for the random conductance model on a supercritical (Bernoulli bond) percolation cluster. The results are also new in the case that the conductivity is constant on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::741f96729a927e84b068ab427afa2c6c
https://doi.org/10.1002/cpa.21726
https://doi.org/10.1002/cpa.21726
Publikováno v:
Grundlehren der mathematischen Wissenschaften ISBN: 9783030155445
We adapt the analysis of previous chapters, based on variational methods, to the case in which the elliptic operator is not necessarily self-adjoint.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51233d7315cbd5e1129f63c0ef1ae1d3
https://doi.org/10.1007/978-3-030-15545-2_10
https://doi.org/10.1007/978-3-030-15545-2_10
Publikováno v:
Grundlehren der mathematischen Wissenschaften ISBN: 9783030155445
We present optimal quantitative estimates for the homogenization of Dirichlet and Neumann boundary-value problems.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::20787e34ad8674b77c84b70124663c83
https://doi.org/10.1007/978-3-030-15545-2_6
https://doi.org/10.1007/978-3-030-15545-2_6
Publikováno v:
Grundlehren der mathematischen Wissenschaften ISBN: 9783030155445
We present quantitative estimates for the homogenization of the parabolic equation $$\begin{aligned} \partial _t u - \nabla \cdot \mathbf {a}(x) \nabla u = 0 \quad \text{ in } \ I\times U \subseteq \mathbb {R}\times {\mathbb {R}^d}. \end{aligned}$$ T
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9745e1feb359b13a2c92bd7e05c9ea11
https://doi.org/10.1007/978-3-030-15545-2_8
https://doi.org/10.1007/978-3-030-15545-2_8