Strong unique continuation for variable coefficient parabolic operators with Hardy type potential

Journal of Differential Equations - Tập 380 - Trang 92-145 - 2024
Agnid Banerjee1, Pritam Ganguly2, Abhishek Ghosh1
1Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore-560065, India
2Institut für Mathematik, Universität Paderborn, 33089 Paderborn, Germany

Tài liệu tham khảo

Almgren, 1979, Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents. Minimal submanifolds and geodesics Aronszajn, 1957, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9), 36, 235 Aronszajn, 1962, A unique continuation theorem for exterior differential forms on Riemannian manifolds, Ark. Mat., 4, 417, 10.1007/BF02591624 Baras, 1984, The heat equation with a singular potential, Trans. Am. Math. Soc., 284, 121, 10.1090/S0002-9947-1984-0742415-3 Banerjee, 2021, A strong unique continuation property for the heat operator with Hardy type potential, J. Geom. Anal., 31, 5480, 10.1007/s12220-020-00487-y Banerjee, 2020, On the strong unique continuation of a degenerate elliptic operator with Hardy type potential, Ann. Mat. Pura Appl. (4), 199, 1, 10.1007/s10231-019-00864-7 Banerjee, 2021, Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation, Discrete Contin. Dyn. Syst., 41, 5105, 10.3934/dcds.2021070 Chanillo, 1990, Unique continuation for Δ+ν and the C. Fefferman-Phong class, Trans. Am. Math. Soc., 318, 275 Escauriaza, 2000, Carleman inequalities and the heat operator, Duke Math. J., 104, 113, 10.1215/S0012-7094-00-10415-2 Escauriaza, 2003, Unique continuation for parabolic operators, Ark. Mat., 41, 35, 10.1007/BF02384566 Escauriaza, 2006, Doubling properties of caloric functions, Appl. Anal., 85, 205, 10.1080/00036810500277082 Escauriaza, 2003, Optimal three-cylinder inequalities for solutions to parabolic equations with Lipschitz leading coefficients, Contemp. Math., 333, 79, 10.1090/conm/333/05955 Garofalo, 1986, Monotonicity properties of variational integrals, Ap weights and unique continuation, Indiana Univ. Math. J., 35, 245, 10.1512/iumj.1986.35.35015 Hörmander, 1983, Uniqueness theorems for second order elliptic differential equations, Commun. Partial Differ. Equ., 8, 21, 10.1080/03605308308820262 Jones, 1977, A fundamental solution for the heat equation which is supported in a strip, J. Math. Anal. Appl., 60, 314, 10.1016/0022-247X(77)90021-X Jerison, 1985, Unique continuation and absence of positive eigenvalues for Schrodinger operators, Ann. Math. (2), 121, 463, 10.2307/1971205 Karadzhov, 1994, Riesz summability of multiple Hermite series in Lp spaces, C. R. Acad. Bulgare Sci., 47, 5 Koch, 2001, Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients, Commun. Pure Appl. Math., 54, 339, 10.1002/1097-0312(200103)54:3<339::AID-CPA3>3.0.CO;2-D Koch, 2009, Carleman estimates and unique continuation for second order parabolic equations with nonsmooth coefficients, Commun. Partial Differ. Equ., 34, 305, 10.1080/03605300902740395 Lieberman, 1996 Lin, 2011, Quantitative uniqueness for second order elliptic operators with strongly singular coefficients, Rev. Mat. Iberoam., 27, 475, 10.4171/RMI/644 Pan, 1992, Unique continuation for Schrodinger operators with singular potentials, Commun. Partial Differ. Equ., 17, 953, 10.1080/03605309208820871 Miller, 1974, Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients, Arch. Ration. Mech. Anal., 54, 105, 10.1007/BF00247634 Necas, 2012, Direct Methods in the Theory of Elliptic Equations Payne, 1958, New bounds for solutions of second order elliptic partial differential equations, Pac. J. Math., 8, 551, 10.2140/pjm.1958.8.551 Plis, 1963, On non-uniqueness in Cauchy problem for an elliptic second order differential equation, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 11, 95 Regbaoui, 1997, Strong uniqueness for second order differential operators, J. Differ. Equ., 141, 201, 10.1006/jdeq.1997.3327 Thangavelu, 1989, Summability of Hermite expansions. I, Trans. Am. Math. Soc., 314, 119, 10.1090/S0002-9947-1989-99923-2 Thangavelu, 1989, Summability of Hermite expansions. II, Trans. Am. Math. Soc., 314, 143, 10.1090/S0002-9947-1989-0958904-7 Vessella, 2003, Carleman estimates, optimal three cylinder inequality, and unique continuation properties for solutions to parabolic equations, Commun. Partial Differ. Equ., 28, 637, 10.1081/PDE-120020491