On the uniqueness for the Cauchy problem for elliptic operators with triple characteristics II

Journal Article · Tue Dec 31 04:00:00 EST 1996 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309608821192· OSTI ID:441142

Fujii, Shin-ichi ^[1]

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1. Kyoto Univ. (Japan)

Let P be an elliptic differential operators of order m with C{sup {infinity}} - coefficients in an open neighborhood {Omega} of the origin in R{sup n}. Let {var_phi} be a real valued C{sup {infinity}} - function on {Omega} with d{var_phi}(0) {plus_minus} 0,{var_phi}(0) = 0. It is said that uniqueness for the Cauchy problem for P with respect to a hypersurface {var_phi}(x) = 0 holds at the origin if for any small open neighborhood {omega} {contained_in} {Omega} of the origin there is an open neighborhood {omega}` {contained_in} {omega} of the origin such that every u {epsilon} C{sup {infinity}}({omega} with Pu = 0,u{parallel}{sub {var_phi}}{>=}0 = 0 vanishes in {omega}`. Uniqueness for the Cauchy problem for elliptic operators has been studied in connection with its unique continuation property. Let P(x,{nu}) = P{sub m}(x,{nu}) + ... + P{sub 0}(x,{nu}) be the symbol of P in a coordinates. Then the roots of the following equation in {tau} are called characteristic roots. P{sub m}(x,{nu} + {tau}d{var_phi}(x)) = 0 {zeta} {epsilon} R{sup n} {backslash} Rd{nu}(x)).

• OSTI ID: 441142
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 3-4 Vol. 21; ISSN 0360-5302; ISSN CPDIDZ
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
CAUCHY PROBLEM
ELLIPTICAL CONFIGURATION
MATHEMATICAL LOGIC
PARTIAL DIFFERENTIAL EQUATIONS