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7 papers · 2 filters
On the evolution of subcritical regions for the Perona-Malik equation
Marina Ghisi, Massimo Gobbino
The Perona-Malik equation is a celebrated example of forward-backward parabolic equation. The forward behavior takes place in the so-called subcritical region, in which the gradien…
An example of global classical solution for the Perona-Malik equation
Marina Ghisi, Massimo Gobbino
We consider the Cauchy problem for the Perona-Malik equation in an open subset of R^{n}, with Neumann boundary conditions. It is well known that in the one-dimensional case this pr…
Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay
Marina Ghisi, Massimo Gobbino
We consider the hyperbolic-parabolic singular perturbation problem for a degenerate quasilinear Kirchhoff equation with weak dissipation. This means that the coefficient of the dis…
Nonexistence of horizontal Sobolev surfaces in the Heisenberg group
Valentino Magnani
Involutivity is a well known necessary condition for integrability of smooth tangent distributions. We show that this condition is still necessary for integrability with Sobolev su…
Endpoint Strichartz estimates for the magnetic Schrodinger equation
Piero D'Ancona, Luca Fanelli, Luis Vega +1
We prove Strichartz estimates for the Schroedinger equation with an electromagnetic potential, in dimension . The decay and regularity assumptions on the potentials are alm…
Existence and multiplicity of stable bound states for the nonlinear Klein-Gordon equation
Claudio Bonanno
We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on…