vesa.julin (at) jyu.fi
Department of Mathematics and Statistics
P.O.Box (MaD)FI-40014 University of Jyvaskyla, Finland.
Associate Professor and Academy Research Fellow (Akatemiatutkija) at the University of Jyväskylä, Finland.
No Teaching at the moment
I am the PhD supervisor of Joonas Niinikoski since spring 2017.
Organizer of the Analysis Seminar in Jyväskylä.
Calculus of Variations and Nonlinear partial differential equations.
 Approximation of BV functions by neural networks: A regularity theory approach, (with B. Avelin), Preprint 2020.
 Stationary sets of the mean curvature flow with a forcing term, (with J. Niinikoski), Preprint 2020.
 Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow, (with J. Niinikoski), Preprint 2020.
 Stationary sets and asymptotic behavior of the mean curvature flow with forcing in the plane, (with N. Fusco and M. Morini), Preprint 2020.
 Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants, (with G. Saracco), Preprint 2020.
 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.
 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.
 Symmetry of minimizers of a Gaussian isoperimetric problem, (with M. Barchiesi), Prob. Theory and Related Fields 177 (2020), 217-256.
 The surface diffusion flow with elasticity in the plane, (with N. Fusco and M. Morini), Comm. Math. Phys., 362 (2018), 571-607.
 Remark on a nonlocal isoperimetric problem, Nonlinear Analysis, 154 (2017), 174-188. (Special edition for Nicola Fusco's 60th birthday).
 Robustness of the Gaussian and the Euclidean concentration, (with M. Barchiesi), Calc Var. PDEs., 56 (2017), 56-80.
 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.
 A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term, (with B. Avelin), J. Funct. Anal., 272 (2017), 3176-3215.
 p-harmonic coordinates for Hölder metrics and applications, (with T. Liimatainen and M. Salo), Comm. in Analysis and Geometry, 25 (2017), 395-430.
 Generalized Harnack inequality for semilinear elliptic equations, J. Math. Pures Appl., (9) 106 (2016), 877-904.
 Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality, (with M. Barchiesi and A. Brancolini), Ann. Probab., 45 (2017), 668-697.
 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.
 On the regularity of critical and minimal sets of a free interface problem, (with N. Fusco), Interfaces Free Bound., 17 (2015), 117-142.
 Generalized Harnack inequality for nonhomogeneous elliptic equations, Arch. Ration. Mech. Anal., 216 (2015), 673-702.
 Minimality via second variation for microphase separation of diblock copolymer melts, (with G. Pisante), J. Reine Angew. Math., 729 (2017), 81-117.
 Isoperimetric problem with a Coulombic repulsive term, Indiana Univ. Math. J., 63 (2014), 77-89.
 A strong form of the Quantitative Isoperimetric inequality, (with N. Fusco), Calc Var. PDEs., 50 (2014), 925-937.
 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.
 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.
 Convexity criteria and uniqueness of absolutely minimizing functions, (with S. Armstrong, M. Crandall and C. Smart), Arch. Ration. Mech. Anal., 200 (2011), 405-443.
 Existence of an absolute minimizer via Perron's method, J. Convex Anal. , 18 (2011), 277-284 .
 Solutions of Aronsson equation near isolated points, Calc Var. PDEs., 37 (2010), 303-328.