showing 3 related works from this author
Rotationally symmetric p -harmonic maps fromD2toS2
2013
We consider rotationally symmetric p-harmonic maps from the unit disk D2⊂R2 to the unit sphere S2⊂R3, subject to Dirichlet boundary conditions and with 1<p<∞. We show that the associated energy functional admits a unique minimizer which is of class C∞ in the interior and C1 up to the boundary. We also show that there exist infinitely many global solutions to the associated Euler–Lagrange equation and we completely characterize them.
Asymptotic behavior for the heat equation in nonhomogeneous media with critical density
2013
Abstract We study the long-time behavior of solutions to the heat equation in nonhomogeneous media with critical singular density | x | − 2 ∂ t u = Δ u , in R N × ( 0 , ∞ ) in dimensions N ≥ 3 . The asymptotic behavior proves to have some interesting and quite striking properties. We show that there are two completely different asymptotic profiles depending on whether the initial data u 0 vanishes at x = 0 or not. Moreover, in the former the results are true only for radially symmetric solutions, and we provide counterexamples to convergence to symmetric profiles in the general case.
Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density
2014
Abstract We study the large time behavior of solutions to the Cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density | x | − 2 ∂ t u = Δ u m , in R N × ( 0 , ∞ ) , where m > 1 and N ≥ 3 , with nonnegative initial condition u ( x , 0 ) = u 0 ( x ) ≥ 0 . The asymptotic behavior proves to have some interesting and striking properties. We show that there are different asymptotic profiles for the solutions, depending on whether the continuous initial data u 0 vanishes at x = 0 or not. Moreover, when u 0 ( 0 ) = 0 , we show the convergence towards a peak-type profile presenting a jump discontinuity, coming from an interesting asymptotic simplification…