T.Carleman 於 1939 年提出了 Carleman type estimates，
對於解的唯一性問題乃是一項不可或缺的工具。
本論文主要依據 Professor V.G.Romanov 在國立成功大學數學系的演講文稿整理而得，而在
L.Hormander 所著的書中曾有提到並加以推導，因此在第二章中，我們先就 Hormander 的方法來推導 Carleman type
estimates，在第三章中，則針對二階線性偏微分算子推導它的 Carleman type estimates。
第四章則為 Carleman type estimates 的應用，其使用範圍相當廣泛，
除了可討論解析延拓的問題，在有關柯西問題的討論上也證明了解的唯一性及穩定性，
最後則證明了反問題解的唯一性。

none

A. L. Bukhgeim, {it Introduction to the theory of inverse problem}, VSP,
Utrecht,2000.

D. Tataru, {it Carleman estimates and unique continuation for solutions to boundary
value problems}, J. Math. Pures Appl. , 75, (1996), 367-408.

D. Tatatu, {it Unique continuation for solutions to PDE's~;~between Hormander's and Holmgren's
theorem}, Comm. part. diff. equations 20 pp. 855-884 (1995).

D. Tataru, {it Unique continuation for operators with partially analytic coefficients},
J. Math. Pures Appl. , 78, (1999), 505-521.

I. Lasiecka, R. Triggiani, P. F. Yao, {it Inverse /observability estimates for second order
elliptic equations with variable coefficients}, J. Math. Anal. Appl. , 235, (1999), 13-57.

I. Lasiecka, J-L. Lions, R. Triggiani, {it Nonhomogeneous boundary value problems for second order hyperbolic equations},
J.Math.Pures Appl., 69, (1986), 149-192.

Izv. Akad., {it On the Cauthy problem for the Laplace equation}, Nauk SSSR Ser. Mat. 20
(1965), 819-842. (Russian)

J.Cheng, V. Isakov, M. Yamamoto, Q. Zhou, {it Lipschitz stability in the lateral Cauchy
problem for elasticity system}, Preprint UTMS 99-33, University of Toyko, Japan, 1999.

L. Hormander, {it A uniqueness of continuation theorem for second order hyperbolic differential
equations}, Comm. part. diff. equations 17 pp. 699-714 (1992).

L. Hormander, {it Linear Partial Differential Operators}, Springer-Verlag, 1963.

L. Hormander, {it The analysis of linear partial differential operators I-IV},
Springer-Verlag, Berlin 1983.

M. Eller, V. Isakov, {it Carleman estimates with two large parameters and
applications}, Proc. of AMS summer research conference in Boulder, CO,
July 1999. Contemporary Math. , AMS 268, 2000, 117-137.

M. V. Klibanov, {it Inverse Problem and Carleman estimates}, Inverse Pronlems, 8, (1992), 576-596.

M. M. Lavrent'ev, V. G. Romanov, S. P. Shishat $cdot$ skii, {it Ill-posed problems of mathematical
physics and analysis}

M. H. Protter, {it Properties of solutions of parabolic equations and inequalities},
Canad. J. Math. 13 (1961), 331-345.

Matthias M. Eller,{it Uniqueness of continuation theorems}, September 1997.

N. Aronszajn, {it A unique continuation theorem for solutions of elliptic partial differential
equations or inequalities of second order}, J. Math. Pures Appl. (9) 36 (1957), 235-249.

T. Carleman, {it Sur un problem d'unicite les systems d'equations aux divees partielles
a deux variables independentes}, Ark. Mat. Astr. Fys., 26B, (1939), 1-9.

V. Isakov, {it Carleman type estimates in an anisotropic case and applications}, J.Diff. Equat.,
105, (1993), 217-239.

Victor Isakov,{it Carleman type estimates and their applications}, September 2000.

V. Isakov, {it Inverse Problems for PDE}, Springer-Verlag, New York, 1997.