On Simple-Layer Potentials for One Class of Pseudodifferential Equations

  • M. M. Osipchuk
  • N. I. Portenko

Abstract

We construct single-layer potentials for a class of pseudodifferential equations connected with symmetric stable stochastic processes. An operator similar to the operator of gradient in the classical potential theory is selected and an analog of the classical theorem on the jump of (co)normal derivative of single-layer potential is established. This result allows us to construct solutions of some initial-boundary-value problems for pseudodifferential equations of the indicated kind.
Published
25.11.2015
How to Cite
OsipchukM. M., and PortenkoN. I. “On Simple-Layer Potentials for One Class of Pseudodifferential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 11, Nov. 2015, pp. 1512-24, http://umj.imath.kiev.ua/index.php/umj/article/view/2086.
Section
Research articles