**Email**

vesa.julin (at) jyu.fi

**Mailing Address**

Department of Mathematics and Statistics

P.O.Box (MaD)FI-40014 University of Jyvaskyla, Finland.

**Affiliation**

Associate Professor and Academy Research Fellow (Akatemiatutkija) at the University of Jyväskylä, Finland.

**Teaching etc...**

No Teaching at the moment

I am the PhD supervisor of Joonas Niinikoski since spring 2017.

Organizer of the Analysis Seminar in Jyväskylä.

**Research interests**

Calculus of Variations and Nonlinear partial differential equations.

**Papers**

[27] Approximation of BV functions by neural networks: A regularity theory approach, (with B. Avelin), Preprint 2020.

[26] Stationary sets of the mean curvature flow with a forcing term, (with J. Niinikoski), Preprint 2020.

[25] Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow, (with J. Niinikoski), Preprint 2020.

[24] Stationary sets and asymptotic behavior of the mean curvature flow with forcing in the plane, (with N. Fusco and M. Morini), Preprint 2020.

[23] Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants, (with G. Saracco), Preprint 2020.

[22] Short time existence of the classical solution to the fractional mean curvature flow, (with D. La Manna), To appear in *Ann. de l'Institut H. Poincare*, Preprint 2019.

[21] The surface diffusion flow with elasticity in three dimensions, (with N. Fusco and M. Morini), To appear in * Arch. Ration. Mech. Anal.* DOI: http://doi.org/10.1007/s00205-020-01532-4.

[20] Symmetry of minimizers of a Gaussian isoperimetric problem, (with M. Barchiesi), *Prob. Theory and Related Fields* **177** (2020), 217-256.

[19] The surface diffusion flow with elasticity in the plane, (with N. Fusco and M. Morini), *Comm. Math. Phys.*, **362** (2018), 571-607.

[18] Remark on a nonlocal isoperimetric problem, *Nonlinear Analysis*, **154** (2017), 174-188. (Special edition for Nicola Fusco's 60th birthday).

[17] Robustness of the Gaussian and the Euclidean concentration, (with M. Barchiesi), *Calc Var. PDEs.*, **56** (2017), 56-80.

[16] Nonlinear stability results for the modified Mullins-Sekerka and the surface diffusion flow, (with E. Acerbi, N. Fusco and M. Morini), *J. Diff. Geom.*, **113** (2019), 1-53.

[15] A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term, (with B. Avelin), * J. Funct. Anal.*, **272** (2017), 3176-3215.

[14] p-harmonic coordinates for Hölder metrics and applications, (with T. Liimatainen and M. Salo), * Comm. in Analysis and Geometry*, **25** (2017), 395-430.

[13] Generalized Harnack inequality for semilinear elliptic equations,* J. Math. Pures Appl.*, (9) **106** (2016), 877-904.

[12] Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality, (with M. Barchiesi and A. Brancolini), * Ann. Probab.*, **45** (2017), 668-697.

[11] Lipschitz regularity for local minimizers of some widely degenerate problems, (with P. Bousquet and L. Brasco), *Ann. Sc. Norm. Super. Pisa Cl. Sci.*, **16** (4) (2016), 1235-1274.

[10] On the regularity of critical and minimal sets of a free interface problem, (with N. Fusco), *Interfaces Free Bound.*, **17** (2015), 117-142.

[9] Generalized Harnack inequality for nonhomogeneous elliptic equations, * Arch. Ration. Mech. Anal.*, **216** (2015), 673-702.

[8] Minimality via second variation for microphase separation of diblock copolymer melts, (with G. Pisante), *J. Reine Angew. Math.*, **729** (2017), 81-117.

[7] Isoperimetric problem with a Coulombic repulsive term, *Indiana Univ. Math. J.*, **63** (2014), 77-89.

[6] A strong form of the Quantitative Isoperimetric inequality, (with N. Fusco), * Calc Var. PDEs.*, **50** (2014), 925-937.

[5] A quantitative second order minimality criterion for cavities in elastic bodies, (with G.M. Capriani and G. Pisante), *SIAM J. Math. Anal.*, **45** (2013), 1952-1991.

[4] A new proof for the equivalence of weak and viscosity solutions for the p-Laplace equation, (with P. Juutinen), * Comm. in PDEs. *, **37** (2012), 934-946.

[3] Convexity criteria and uniqueness of absolutely minimizing functions, (with S. Armstrong, M. Crandall and C. Smart), * Arch. Ration. Mech. Anal.*, **200** (2011), 405-443.

[2] Existence of an absolute minimizer via Perron's method, *J. Convex Anal. *, **18** (2011), 277-284 .

[1] Solutions of Aronsson equation near isolated points, * Calc Var. PDEs.*, **37** (2010), 303-328.