Sharp L p Carleman estimates and unique continuation

David Dos Santos Ferreira

Journées équations aux dérivées partielles (2003)

  • page 1-12
  • ISSN: 0752-0360

Abstract

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We will present a unique continuation result for solutions of second order differential equations of real principal type P ( x , D ) u + V ( x ) u = 0 with critical potential V in L n / 2 (where n is the number of variables) across non-characteristic pseudo-convex hypersurfaces. To obtain unique continuation we prove L p Carleman estimates, this is achieved by constructing a parametrix for the operator conjugated by the Carleman exponential weight and investigating its L p - L p ' boundedness properties.

How to cite

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Dos Santos Ferreira, David. "Sharp $L^p$ Carleman estimates and unique continuation." Journées équations aux dérivées partielles (2003): 1-12. <http://eudml.org/doc/93448>.

@article{DosSantosFerreira2003,
abstract = {We will present a unique continuation result for solutions of second order differential equations of real principal type $P(x,D)u+V(x)u=0$ with critical potential $V$ in $L^\{n/2\}$ (where $n$ is the number of variables) across non-characteristic pseudo-convex hypersurfaces. To obtain unique continuation we prove $L^p$ Carleman estimates, this is achieved by constructing a parametrix for the operator conjugated by the Carleman exponential weight and investigating its $L^p-L^\{p^\{\prime \}\}$ boundedness properties.},
author = {Dos Santos Ferreira, David},
journal = {Journées équations aux dérivées partielles},
keywords = {parametrix; - boundedness},
language = {eng},
pages = {1-12},
publisher = {Université de Nantes},
title = {Sharp $L^p$ Carleman estimates and unique continuation},
url = {http://eudml.org/doc/93448},
year = {2003},
}

TY - JOUR
AU - Dos Santos Ferreira, David
TI - Sharp $L^p$ Carleman estimates and unique continuation
JO - Journées équations aux dérivées partielles
PY - 2003
PB - Université de Nantes
SP - 1
EP - 12
AB - We will present a unique continuation result for solutions of second order differential equations of real principal type $P(x,D)u+V(x)u=0$ with critical potential $V$ in $L^{n/2}$ (where $n$ is the number of variables) across non-characteristic pseudo-convex hypersurfaces. To obtain unique continuation we prove $L^p$ Carleman estimates, this is achieved by constructing a parametrix for the operator conjugated by the Carleman exponential weight and investigating its $L^p-L^{p^{\prime }}$ boundedness properties.
LA - eng
KW - parametrix; - boundedness
UR - http://eudml.org/doc/93448
ER -

References

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