Let $Lu = f$ be satisfied on a bounded domain $\Omega \subset \mathbb{R}^n$ with smooth boundary $\partial \Omega$, where $L$ is a strongly elliptic second order differential operator with real analytic coefficients in the interior $\Omega$. $u$ and $f$ are real analytic in the interior $\Omega$ and both are smooth up to the boundary, with zero Dirichlet boundary data $u|_{\partial \Omega} = f|_{\partial \Omega} = 0$. Suppose in addition we assume that $u$ satisfies zero Neumann data $ \frac{\partial u}{\partial \eta}|_{\partial \Omega} = 0$.

I am looking for references which give unique continuation results like $u = f = 0$. I am not sure if we need additional restrictions on $L$ to ensure such a conclusion (I am happy with references that say something about $L = \Delta$). Any pointers will be highly appreciated.

New contributor
user131136 is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
  • 1
    Aronszajn, N. 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. – Liviu Nicolaescu Nov 8 at 18:54
  • @LiviuNicolaescu I cannot seem to find the Aronszajn paper anywhere online. Is it a particular result there that you are referring to, or is it a general technique that I can may be locate somewhere else? Thanks a lot ! – user131136 Nov 9 at 12:35
  • I have access only to hardcopies of the journal. Read the MathSciNet review. It describes precisely Aronszajn's result. mathscinet.ams.org/mathscinet/pdf/… – Liviu Nicolaescu Nov 9 at 14:00

Your Answer

user131136 is a new contributor. Be nice, and check out our Code of Conduct.
 
discard

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.