Vesa Julin

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.