- Bistable elliptic equations with fractional diffusion

- Cinti, Eleonora <1982>

- MAT/05 Analisi matematica

- This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

- 2010-07-05

- Doctoral Thesis

- PeerReviewed

- application/pdf

urn:nbn:it:unibo-2284

Cinti, Eleonora (2010) Bistable elliptic equations with fractional diffusion, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica