Geometric regularity theory for fully nonlinear elliptic equations
 
 
Description:  In this talk, we examine the regularity theory for fully nonlinear elliptic equations of the form F(D^2 u)=f(x) where F is a (λ,Λ)-elliptic operator and f:B1→ℝ is a continuous source term, in appropriate Lebesgue spaces. We recur to a set of tools known as geometric- tangential analysis to produce a priori estimates for the solutions in Sobolev spaces, under minimal (asymptotic) assumptions on the operator F. In addition, we discuss regularity in p-BMO spaces and the density of W2,p- solutions in the class of continuous viscosity solutions. We conclude the talk with the study of a degenerate problem; in this case, we produce a result on the optimal regularity of solutions in Holder spaces.
Date:  2016-12-07
Start Time:   14:30
Speaker:  Edgard A. Pimentel (Univ. São Carlos, Brazil)
Institution:  Universidade Federal de São Carlos, Brazil
Place:  Sala 5.4
Research Groups: -Analysis
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