The C^{p'}-regularity conjecture in the plane
 
 
Description:  We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C^{p'}=C^{1,\frac{1}{p-1}}; this regularity is optimal. This is a joint work with E. Teixeira (UFC, Brazil) and J.M. Urbano (UC, Portugal).
Date:  2016-11-25
Start Time:   14:30
Speaker:  Damião Araújo (UNILAB and UFPB, Brazil)
Institution:  UNILAB and UFPB, Brazil
Place:  Sala 5.5
Research Groups: -Analysis
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