Unique continuation for parabolic operators
Tóm tắt
Từ khóa
Tài liệu tham khảo
Adolfson, V. andEscauriaza, L.,C 1·α domains and unique continuation at the boundary.Comm. Pure Appl. Math. 50 (1997), 935–969.
Ahlfors, L. V.,Complex Analysis, 3rd ed., McGraw-Hill, New York, 1966.
Aronszajn, N., Krzywicki, A. andSzarski, J., A unique continuation theorem for exterior differential forms on Riemannian manifolds,Ark. Mat. 4 (1962), 417–453.
Chen, X. Y., A strong unique continuation theorem for parabolic equations,Math. Ann. 311 (1996), 603–630.
Escauriaza, L. andVega, L., Carleman inequalities and the heat operator II,Indiana Univ. Math. J. 50 (2001), 1149–1169.
Evans, L. G.,Partial Differential Equations, Amer. Math. Soc., Providence, R. I., 1998.
Grisvard, P.,Elliptic Problems in Nonsmooth Domains, Pitman, Boston. Mass., 1985.
Hörmander, L., Uniqueness theorems for second order elliptic differential equations,Comm. Partial Differential Equations 8 (1983), 21–64.
Kenig, C. E. andWang, W., A note on boundary unique continuation for harmonic functions in non-smooth domains,Potential Anal. 8 (1998), 143–147.
Ladyzhenskaya, O. A., Solonnikov, V. A. andUraltseva, N. N.,Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1968 (Russian). English transl.: Translations of Math. Monographs23, Amer. Math. Soc., Providence, R. I., 1968.
Landis, E. M. andOleinik, O. A., Generalized analyticity and some related properties of solutions of elliptic and parabolic equations,Uspekhi Mat. Nauk 29(176):2 (1974), 190–206 (Russian). English transl.:Russian Math. Surveys 29 (1974), 195–212.
Lin, F. H., A uniqueness theorem for parabolic equations,Comm. Pure Appl. Math. 42 (1988), 125–136.
Miller, K., Non-unique continuation for certain ode’s in Hilbert space and for uniformly parabolic and elliptic equations in self-adjoint divergence form,Arch. Rational Mech. Anal. 54 (1963), 105–117.
Plis, A., On non-uniqueness in Cauchy problems for an elliptic second order differential equation,Bull. Acad. Polon. Sci. Math. Astronom. Phys. 11 (1963), 95–100.
Poon, C. C., Unique continuation for parabolic equations,Comm. Partial Differential Equations 21 (1996), 521–539.
Saut, J. C. andScheurer, E., Unique continuation for evolution equations,J. Differential Equations 66 (1987). 118–137.