Doubling properties of caloric functions

References

• Garofalo , N and Lin , FH . 1986 . Monotonicity properties of variational integrals, A p -weights and unique continuation . Indiana University Mathematics Journal , 35 : 245 – 267 .
   Web of Science ®Google Scholar
• Landis , EM and Oleinik , OA . 1974 . Generalized analyticity and some related properties of solutions of elliptic and parabolic equations . Russian Mathematical Surveys , 29 : 195 – 212 .
   Google Scholar
• Lin , FH . 1988 . A uniqueness theorem for parabolic equations . Communications on Pure and Applied Mathematics , 42 : 125 – 136 .
   Google Scholar
• Alessandrini , G , Beretta , E , Rosset , E and Vessella , S . 2001 . Optimal stability for inverse elliptic boundary value problems with unknown boundary . Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV , XXIX ( n.2 ) : 755 – 806 .
   Google Scholar
• Alessandrini , G , Morassi , A and Rosset , E . 2003 . Size estimates, Inverse Problems: Theory and Applications, Contemporary Mathematics , Edited by: Alessandrini , G and Uhlmann , G . Vol. 333 , 1 – 34 . American Mathematical Society . (Eds.)
   Google Scholar
• Canuto , B , Rosset , E and Vessella , S . 2002 . Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries . American Mathematical Society Translations , 354 ( n.2 ) : 491 – 535 .
   Web of Science ®Google Scholar
• Poon , CC . 1996 . Unique continuation for parabolic equations . Comm. Part. Diff. Equat. Appl. Math. , 21 : 521 – 539 .
   Web of Science ®Google Scholar
• Chen , XY . 1996 . A strong unique continuation theorem for parabolic equations . Mathematische Annalen , 311 : 603 – 630 .
   Web of Science ®Google Scholar
• Escauriaza , L . 2000 . Carleman inequalities and the heat operator . Duke Mathematical Journal , 104 ( n.1 ) : 113 – 127 .
   Web of Science ®Google Scholar
• Escauriaza , L and Vega , L . 2001 . Carleman inequalities and the heat operator II . Indiana University Mathematics Journal , 50 ( n.3 ) : 1149 – 1169 .
   Web of Science ®Google Scholar
• Escauriaza , L and Fernández , FJ . 2003 . Unique continuation for parabolic operators . Arkiv for Matematik , 41 : 35 – 60 .
   Web of Science ®Google Scholar
• Fernández , FJ . 2003 . Unique continuation for parabolic operators II . Comm. Part. Diff. Equat. , 28 ( n. 9&10 ) : 1597 – 1604 .
   Web of Science ®Google Scholar
• Alessandrini , G and Vessella , S . 2003 . Remark on the strong unique continuation property for parabolic equations . Proceedings of the American Mathematical Society , 132 ( n.2 ) : 499 – 501 .
   Web of Science ®Google Scholar
• Lady[zbreve]enskaja , OA and Solonnikov , VA . 1968 . “ Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs ” . In American Mathematical Society Vol. 23 , Providence, RI
   Google Scholar
• Aronson , DG . 1967 . Bounds for the fundamental solution of parabolic equations . Bull. of the Amer. Math. Soc. , 73 : 890 – 896 .
   Web of Science ®Google Scholar
• Miller , K . 1963 . Non-unique continuation for certain ode's in Hilbert space and for uniformly parabolic and elliptic equations in self-adjoint divergence form . Arch. Rat. Mech. Anal. , 54 : 105 – 117 .
   Google Scholar
• Pucci , C . 1959 . Alcune limitazioni per le soluzioni di equazioni paraboliche . Ann. Mat. Pura Appl. , IV ( Ser. 48 ) : 161 – 172 .
   Google Scholar
• Saut , JC and Scheurer , E . 1987 . Unique continuation for evolution equations . Journal of Differential Equations , 66 : 118 – 137 .
   Web of Science ®Google Scholar
• Sogge , CD . 1990 . A unique continuation theorem for second order parabolic differential operators . Arkiv for Matematik , 28 : 159 – 182 .
   Web of Science ®Google Scholar