Zobrazeno 1 - 10
of 199
pro vyhledávání: '"Kuusi, Tuomo"'
Autor:
Avelin, Benny, Kuusi, Tuomo, Nummi, Patrik, Saksman, Eero, Tölle, Jonas M., Viitasaari, Lauri
We study periodic solutions to the following divergence-form stochastic partial differential equation with Wick-renormalized gradient on the $d$-dimensional flat torus $\mathbb{T}^d$, \[ -\nabla\cdot\left(e^{\diamond (- \beta X) }\diamond\nabla U\rig
Externí odkaz:
http://arxiv.org/abs/2405.17195
Autor:
Armstrong, Scott, Kuusi, Tuomo
We prove a quantitative estimate on the homogenization length scale in terms of the ellipticity ratio~$\Lambda/\lambda$ of the coefficient field. This upper bound applies to high-contrast elliptic equations demonstrating near-critical behavior. Speci
Externí odkaz:
http://arxiv.org/abs/2405.10732
We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case includes
Externí odkaz:
http://arxiv.org/abs/2404.01115
Autor:
Avelin, Benny, Kuusi, Tuomo, Nummi, Patrik, Saksman, Eero, Tölle, Jonas M., Viitasaari, Lauri
We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and th
Externí odkaz:
http://arxiv.org/abs/2402.09127
We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and H\"older spaces as well as pointwise bounds of the gradient in terms of Riesz potentials, leading to fine regularity results in man
Externí odkaz:
http://arxiv.org/abs/2212.01950
Autor:
Armstrong, Scott, Kuusi, Tuomo
We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation also contains new results, such as optimal estimates (both in terms of
Externí odkaz:
http://arxiv.org/abs/2210.06488
Autor:
Aleksanyan, Gohar, Kuusi, Tuomo
In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both for the solution and the free boundary for the heterogeneous obstacle
Externí odkaz:
http://arxiv.org/abs/2112.10879
We prove a quantitative, large-scale doubling inequality and large-scale three-ellipsoid inequality for solutions of uniformly elliptic equations with periodic coefficients. These estimates are optimal in terms of the minimal length scale on which th
Externí odkaz:
http://arxiv.org/abs/2107.14248
Publikováno v:
J. Differential Equations 279 (2021), 245--281
In this paper, we study a doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow. In the special case p=2 our theory includes the classical Yamabe flow on a bounded domain in Eucli
Externí odkaz:
http://arxiv.org/abs/2103.15817
Publikováno v:
J. Geom. Anal. 30 (2020), no. 2, 1918--1964
We study doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow from now on, which includes the classical Yamabe flow on a bounded domain in Euclidean space in the special case p=2
Externí odkaz:
http://arxiv.org/abs/2103.15259