17 citations · 45 across the 19 of their papers we have counts for
22 papers
Regularity of soda-can domains for the -parabolic equation
Benny Avelin, Mikko Parviainen
We classify the regularity of the origin for the -parabolic equation in the soda-can domains $$Θ_{l,θ}=\{(x,t)\in\mathbb{R}^n\times\mathbb{R}:0 < -t < θ|x|^l < θ\},\text{ where…
-cut-off phenomenon for Galerkin projections of Fokker-Planck equations with monomial potentials
Benny Avelin, Gerardo Barrera
In this manuscript, we establish the existence/non-existence of the cut-off phenomenon for the Langevin--Kolmogorov random dynamics with monomial convex potentials, possible singul…
Coarse-grained ellipticity and De Giorgi-Nash-Moser theory
Scott Armstrong, Benny Avelin, Cristiana De Filippis +2
We prove local boundedness and a Harnack inequality for nonnegative weak solutions of the equation under a coarse-grained ellipticity assump…
Renormalized stochastic pressure equation with log-correlated Gaussian coefficients
Benny Avelin, Tuomo Kuusi, Patrik Nummi +3
We study periodic solutions to the following divergence-form stochastic partial differential equation with Wick-renormalized gradient on the -dimensional flat torus $\mathbb{T}^…
Weak and Perron Solutions for Stationary Kramers-Fokker-Planck Equations in Bounded Domains
Benny Avelin, Mingyi Hou
In this paper, we investigate weak solutions and Perron-Wiener-Brelot solutions to the linear stationary Kramers-Fokker-Planck equation in bounded domains. We establish the existen…
1D stochastic pressure equation with log-correlated Gaussian coefficients
Benny Avelin, Tuomo Kuusi, Patrik Nummi +3
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 we…
On the Impact of Approximation Errors on Extreme Quantile Estimation with Applications to Functional Data Analysis
Jaakko Pere, Benny Avelin, Valentin Garino +2
We study the effect of approximation errors in assessing the extreme behavior of heavy-tailed random objects. We give conditions for the approximation error such that the standard…
A Galerkin type method for kinetic Fokker Planck equations based on Hermite expansions
Benny Avelin, Mingyi Hou, Kaj Nyström
In this paper, we develop a Galerkin-type approximation, with quantitative error estimates, for weak solutions to the Cauchy problem for kinetic Fokker-Planck equations in the doma…
Concentration inequalities for leave-one-out cross validation
Benny Avelin, Lauri Viitasaari
In this article we prove that estimator stability, together with a gradient-growth condition on the expected fitted loss, is enough to provide concentration bounds for leave-one-ou…
A note on the capacity estimate in metastability for generic configurations
Benny Avelin, Vesa Julin
In this paper we further develop the ideas from Geometric Function Theory initially introduced in [arXiv:2206.13206], to derive capacity estimate in metastability for arbitrary con…
Geometric Characterization of the Eyring-Kramers Formula
Benny Avelin, Vesa Julin, Lauri Viitasaari
In this paper we consider the mean transition time of an over-damped Brownian particle between local minima of a smooth potential. When the minima and saddles are non-degenerate th…
Remarks on existence and uniqueness of the solution for stochastic partial differential equations
Benny Avelin, Lauri Viitasaari
In this article we consider existence and uniqueness of the solutions to a large class of stochastic partial differential of form , dri…
Approximation of BV functions by neural networks: A regularity theory approach
Benny Avelin, Vesa Julin
In this paper we are concerned with the approximation of functions by single hidden layer neural networks with ReLU activation functions on the unit circle. In particular, we are i…
Neural ODEs as the Deep Limit of ResNets with constant weights
Benny Avelin, Kaj Nyström
In this paper we prove that, in the deep limit, the stochastic gradient descent on a ResNet type deep neural network, where each layer shares the same weight matrix, converges to t…
Boundary behavior of solutions to the parabolic p-Laplace equation II
Benny Avelin
This paper is the second installment in a series of papers concerning the boundary behavior of solutions to the -parabolic equations. In this paper we are interested in the shor…
Boundary behavior of solutions to the parabolic p-Laplace equation
Benny Avelin, Kaj Nyström, Tuomo Kuusi
We establish boundary estimates for non-negative solutions to the p-parabolic equation in the degenerate range . Our main results include new parabolic intrinsic Harnack chain…
Characterizations of interior polar sets for the degenerate p-parabolic equation
Benny Avelin, Olli Saari
This paper deals with different characterizations of sets of nonlinear parabolic capacity zero, with respect to the parabolic p-Laplace equation. Specifically we prove that certain…
A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term
Benny Avelin, Vesa Julin
This paper concerns the boundary behavior of solutions of certain fully nonlinear equations with a general drift term. We elaborate on the non-homogeneous generalized Harnack inequ…
A comparison principle for the porous medium equation and its consequences
Benny Avelin, Teemu Lukkari
We prove a comparison principle for the porous medium equation in more general open sets in than space-time cylinders. We apply this result in two related contex…
Boundary Estimates for Certain Degenerate and Singular Parabolic Equations
Benny Avelin, Ugo Gianazza, Sandro Salsa
We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic -Laplacian. Assuming that such s…
Lower semicontinuity of weak supersolutions to the porous medium equation
Benny Avelin, Teemu Lukkari
Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower se…
Harnack estimates for degenerate parabolic equations modeled on the subelliptic p-Laplacian
Benny Avelin, Luca Capogna, Giovanna Citti +1
We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype {equation*} \partial_tu= -\sum_{i=1}^{m}X_i^\ast (|\X u|^{p-2} X_i u){equation*} where $p…