# Benny Avelin

### Preprints

Deep limits and cut-off phenomena for neural networks, with A. Karlsson, 2021, arXiv.

Remarks on existence and uniqueness of the solution for stochastic partial differential equations, with L. Viitasaari, 2021, arXiv.

Uncertainty-Aware Body Composition Analysis with Deep Regression Ensembles on UK Biobank MRI, T. Langner, F. K. Gustafsson, B. Avelin, R. Strand, H. Ahlström, J. Kullberg, 2021, arXiv.

Approximation of BV functions by neural networks: A regularity theory approach, with V. Julin, 2020, arXiv

### Publications

Neural ODEs as the Deep Limit of ResNets with constant weights, with K. Nyström, 2019, arXiv, available online Analysis and Applications doi. Code.

Boundary behavior of solutions to the parabolic p-Laplace equation II, Journal of Functional Analysis, 2020, arXiv.

Boundary behavior of solutions to the parabolic p-Laplace equation, with T. Kuusi and K. Nyström,

*Anal. PDE*12 (2019), no. 1, 1–42.Nonlinear Calderón-Zygmund in the limiting case, with T. Kuusi and G. Mingione, Arch Rational Mech Anal (2017).

*A comparison principle for the porous medium equation and its consequences*, with T. Lukkari, Revista Matemática Iberoamericana 33(2):573-594, 2017*A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term,*with V. Julin, Journal of Functional Analysis, 2016.*Characterizations of interior polar sets for the degenerate p-parabolic equation, with Saari, O.,**Journal of Evolution Equations**, 2016.**Boundary Estimates for Certain Degenerate and Singular Parabolic Equations*, with Gianazza U. and Salsa S., Journal of European Mathematical Society, 18(2):381-426, 2016.*On time dependent domains for the degenerate p-parabolic equation: Carleson estimate and Hölder continuity*, Mathematische Annalen, 364(1):667-686, 2016. (Erratum)*Approximation of Plurisubharmonic Functions*, with Hed L. and Persson H., Complex Variables and Elliptic Equations, 61(1):23-28, 2016.*A note on the hyperconvexity of pseudoconvex domains beyond Lipschitz regularity*, with Hed L. and Persson H., Potential Analysis, 43(3):531-545, 2015.*Variational parabolic capacity*, with Kuusi T. and Parviainen M., Discrete and Continuous Dynamical Systems - Series A, 35(12):5665-5688, 2015.*Lower semicontinuity of weak supersolutions to the porous medium equation*, with Lukkari T., Proceedings of the American Mathematical Society, 143(8):3475-3486, 2015.*Harnack estimates for degenerate parabolic equations modeled on the subelliptic p-Laplacian*, with Capogna L., Citti G., Nyström K., Advances in Mathematics, 257:25-65, 2014.*Estimates for Solutions to Equations of p-Laplace type in Ahlfors regular NTA-domains*, with Nyström K., J. Funct. Anal. 266(9):5955-6005, 2014.*Wolff-potential estimates and doubling of subelliptic p-harmonic measures*, with Nyström K., Nonlinear Anal. 85:145-159, 2013.*On a one-phase free boundary problem*, Ann. Acad. Sci. Fenn. Math. 38(1):181-191, 2013.*Optimal doubling, Reifenberg flatness and operators of p-Laplace type*, with Lundström N.L.P. and Nyström K., Nonlinear Anal. 74(17):5943-5955, 2011.*Boundary estimates for solutions to operators of p-Laplace type with lower order terms*, with Lundström N.L.P. and Nyström K., J. Differential Equations 250(1):264-291, 2011.

### Other

*Boundary Behavior of p-Laplace Type Equations*, Doctoral thesis (2013), Kappa.*Approximation and Bounded Plurisubharmonic Exhaustion Functions Beyond Lipschitz Domains*, with Hed L. and Persson H., arXiv, 2012. Never published and split into**"****A note on the hyperconvexity of pseudoconvex domains beyond Lipschitz regularity****"****Potential Analysis****, 2015;**and**"****Approximation of Plurisubharmonic Functions****"****Complex Variables and Elliptic Equations****, 2015.**