TY - JOUR
AU - M. M. Osipchuk
AU - N. I. Portenko
PY - 2015/11/25
Y2 - 2020/12/05
TI - On Simple-Layer Potentials for One Class of Pseudodifferential Equations
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 11
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/2086
AB - 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.
ER -