Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Strong solutions to an elliptic obstacle problem with coefficients in VMO

Tuesday, February 28, 2012 at 11:30am - 12:30pm

Speaker: Kubrom Teka, Kansas State University

We consider the obstacle problem:

a^{ij}D_{ij}w = Chi_{w > 0} in B_1

with

w = psi on partial B_1

where we assume that the coefficients $a^{ij}$ belong to VMO, that the functions $w, psi geq 0$ belong to the Sobolev space $W^{2,p},$ and that $w$ satisfies the PDE pointwise almost everywhere. We show existence, uniqueness, regularity, and nondegeneracy of the solutions. These results allow us to begin the study of the regularity of the free boundary. In particular, we establish a measure theoretic version of the Caffarelli Alternative after showing a measure stability result for the contact sets. (This is a joint work with Ivan Blank.)

Speaker: Kubrom Teka, Kansas State University

Location   Hill 705