Siva Athreya - Existence of Positive Solutions Satisfying the Boundary Harnack Principle for a Semi-linear Dirichlet Problem

Boundary Harnack principle is a key tool in obtaining many results in classical potential theory. Suppose D is a smooth domain and u and v are two positive harmonic functions on D that vanish on a subset A of . The boundary Harnack principle says that u and v tend to zero at the same rate. Over the past three decades, there has been a lot of research on extending the principle to very general domains. Another natural question is, does the boundary Harnack principle hold for solutions of elliptic partial differential equations other than ? We shall investigate the above question in our talk. This was part of my Ph.D. thesis work with Professor K. Burdzy, at the University of Washington.