Seminar talk: Prof. Dmitry Khavinson from USF
Abstract: How far does the Newtonian potential of a solid bounded by an algebraic surface extend inside the solid? Why is the celebrated Schwarz reflection principle never discussed in dimensions higher than 2? How does one find singularities of an axially symmetric harmonic function in the ball from the coefficients in its expansion by spherical harmonics? If a line intersects a domain over two disjoint segments and a harmonic function in the domain vanishes on one, does it have to vanish on the other one? We shall discuss these questions in the unified light of analytic continuation of solutions to linear analytic pde. The talk will be accessible to undergraduate and graduate students majoring in math, physics and engineering.