8 citations · 23 across the 9 of their papers we have counts for
11 papers
On the parabolic Harnack inequality for non-local diffusion equations
Dominik Dier, Jukka Kemppainen, Juhana Siljander +1
We settle the open question concerning the Harnack inequality for globally positive solutions to non-local in time diffusion equations by constructing a counter-example for dimensi…
Boundary regularity for the porous medium equation
Anders Björn, Jana Björn, Ugo Gianazza +1
We study the boundary regularity of solutions to the porous medium equation in the degenerate range . In particular, we show that in cylinders the Dirichlet probl…
Sharp Regularity for Weak Solutions to the Porous Medium Equation
Ugo Gianazza, Juhana Siljander
Let be a nonnegative, local, weak solution to the porous medium equation for in a space-time cylinder . Fix a point : if the average \[ a{\buildre…
On the interior regularity of weak solutions to the 2-D incompressible Euler equations
Juhana Siljander, José Miguel Urbano
We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrabili…
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
Jukka Kemppainen, Juhana Siljander, Rico Zacher
We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classic…
Everywhere differentiability of viscosity solutions to a class of Aronsson's equations
Juhana Siljander, Changyou Wang, Yuan Zhou
For any open set and , we establish everywhere differentiability of viscosity solutions to the Aronsson equation $$ <D_x(H(x, Du)), D_p H(x, Du)>=0 \q…