Vesa Julin

vesa.julin (at)

Mailing Address
Department of Mathematics and Statistics
P.O.Box (MaD)FI-40014 University of Jyvaskyla, Finland.


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


PDE 2 in the Spring 2018.

Research interests

Nonlinear partial differential equations and Calculus of Variations.


The surface diffusion flow with elasticity in three dimensions, (with N. Fusco and M. Morini), Preprint 2018.

Symmetry of minimizers of a Gaussian isoperimetric problem, (with M. Barchiesi), Preprint 2018.

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), To appear in J. Diff. Geom., Preprint 2016.

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), Communications in Analysis and Geometry, 25 (2017), 395-430.

Generalized Harnack inequality for semilinear elliptic equations, J. Math. Pures Appl., (9) 106 (2016), 877-904. (The recent arxiv version contains some corrections with respect to the Journal version)

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.