CONTINUATION PROBLEM FOR HARMONIC FUNCTION IN THE BALL
Abstract
The analytical continuation problem and Cauchy problem for the elliptic equations,
a so-called Adamar example, have appeared important problems in geophysics in
connection with questions of potential fields continuation. Bavrin I.I. has offered the formulas
restoring analytical or harmonious function on its values on an internal circle for
areas with circular symmetry of E2 . The analytical decision of a problem of harmonious
function continuation in an individual-dimensional sphere on its known values on internal
sphere is found. The decision of a similar continuation problem in case of the task on
sphere not the function, and its some operational transformations is received.
a so-called Adamar example, have appeared important problems in geophysics in
connection with questions of potential fields continuation. Bavrin I.I. has offered the formulas
restoring analytical or harmonious function on its values on an internal circle for
areas with circular symmetry of E2 . The analytical decision of a problem of harmonious
function continuation in an individual-dimensional sphere on its known values on internal
sphere is found. The decision of a similar continuation problem in case of the task on
sphere not the function, and its some operational transformations is received.
About the Authors
О. Яремко
Пензенский государственный педагогический университет
имени В.Г. Белинского
Russian Federation
Russian Federation
Ю. Парфёнова
Пензенский государственный педагогический университет
имени В.Г. Белинского
Russian Federation
Russian Federation
References
1. Баврин, И.И. Обратная задача для интегральной формулы Коши в кольце[Текст]. - Доклады РАН, 2009. Т.428 №2 - С. 151-152.
2. Баврин, И.И. Операторный метод в комплексном анализе [Текст]. - М.: Прометей, 1991. - 200с.
3. Лаврентьев, М.М.; Романов, В.Г.; Васильев, Г.В. Многомерные обратные задачи для дифференциальных уравнений [Текст]. - Новосибирск.: Наука, 1967.
4. Никифоров, А.Ф.; Уваров, В.Б. Специальные функции математической физики - 2 изд [Текст]. - М.: 1984.
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