Тип публикации: статья из журнала
Год издания: 2009
Ключевые слова: ill-posed Cauchy problem, Carleman's formulas
Аннотация: Let D be a bounded domain in R-n (n >= 2) with infinitely smooth boundary. D. We give some necessary and sufficient conditions for the Cauchy problem to be solvable in the Lebesgue space L-2(D) in D for an arbitrary differential operator A having an injective principal symbol. Furthermore, using bases with double orthogonality, we Показать полностьюconstruct Carleman's formula that restores a (vector-)function in L-2(D) from the Cauchy data given on a relatively open connected set G.. D and the values Au in D whenever the data belong to L-2(G) and L-2(D) respectively.
Журнал: SIBERIAN MATHEMATICAL JOURNAL
Выпуск журнала: Vol. 50, Is. 3
Номера страниц: 547-559
ISSN журнала: 00374466
Место издания: NEW YORK
Издатель: CONSULTANTS BUREAU/SPRINGER