# Benny Avelin

### Preprints

Preprints

- Neural ODEs as the Deep Limit of ResNets with constant weights, with K. Nyström, 2019, arXiv. Code.
- Boundary behavior of solutions to the parabolic p-Laplace equation II, 2018, arXiv.

### Publications

Publications

- 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

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**"**and*A note on the hyperconvexity of pseudoconvex domains beyond Lipschitz regularity*" Potential Analysis, 2015;**"***Approximation of Plurisubharmonic Functions*" Complex Variables and Elliptic Equations, 2015.