Abstract
We consider the Perona-Malik equation in an open set Ω ⊆ ℝ n , with initial and Neumann boundary conditions. It is well known that in the one-dimensional case this problem does not admit any global C 1 solution if the initial condition u 0 is transcritical, namely when |∇u 0(x)| −1 is a sign changing function in Ω. In this paper we show that this result cannot be extended to higher dimension. We show indeed that for n ≥ 2 the problem admits radial solutions of class C 2, 1 with a transcritical initial condition.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
