Seminars: V. P. Mikhailov, On the existence of limit values on the boundary for solutions of elliptic equations

SEMINARS


Steklov Mathematical Institute Seminar February 15, 2001, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)

On the existence of limit values on the boundary for solutions of elliptic equations V. P. Mikhailov
Abstract: Let $u(x)=u(x_1,\dots,x_n)$ be a solution of the elliptic equation $$ \Delta^mu+P(i\partial/{\partial x})u=0, $$ in a strip, where $m\ge1$ and $P(\xi)$ is an arbitrary polynomial with constant coefficients of degree at most $2m-1$. Necessary and sufficient conditions are found for the existence of $W_2^k$-limit values of the function $u(x)$ on the boundary for arbitrary real $k$.