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I added the definition of overdetermined ellipticity.
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user38064
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On a closed manifold $M$, let $P(f)=0$ be a linear overdetermined elliptic smoothsystem of PDE of 2nd order; fororder with smooth coefficients. By overdetermined ellipticity, I mean the principal sympbol is injective. For simplicity, let's assume it is for a real-valued function $f$. If a solution $f$ is zero on an open subset, then is $f$ zero on the whole of $M$? If this is not true in general, what would be conditions for it to be true? Also please recommend some references. Thanks a lot!

On a closed manifold $M$, let $P(f)=0$ be a linear overdetermined elliptic smooth PDE of 2nd order; for simplicity, let's assume it is for a real-valued function $f$. If a solution $f$ is zero on an open subset, then is $f$ zero on the whole of $M$? If this is not true in general, what would be conditions for it to be true? Also please recommend some references. Thanks a lot!

On a closed manifold $M$, let $P(f)=0$ be a linear overdetermined elliptic system of PDE of 2nd order with smooth coefficients. By overdetermined ellipticity, I mean the principal sympbol is injective. For simplicity, let's assume it is for a real-valued function $f$. If a solution $f$ is zero on an open subset, then is $f$ zero on the whole of $M$? If this is not true in general, what would be conditions for it to be true? Also please recommend some references. Thanks a lot!

LaTeX and grammar cleanup
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edit approved Aug 2, 2013 at 10:42
Branimir Ćaćić
edit approved Aug 2, 2013 at 10:42
Branimir Ćaćić
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On a closed manifold M$M$, let P(f)=0$P(f)=0$ be a linear overdetermined elliptic smooth PDE of 2nd order.(Fororder; for simplicity, let's assume it is for a real-valued function f$f$.) If a solution f$f$ is zero on an open subset, then is f$f$ zero on the whole Mof $M$? If this is not true in general, what would be conditions for it to be true? Also please recommend some references. Thanks a lot!

On a closed manifold M, let P(f)=0 be a linear overdetermined elliptic smooth PDE of 2nd order.(For simplicity, let's assume it is for a real-valued function f.) If a solution f is zero on an open subset, then is f zero on the whole M? If not in general, what would be conditions for it to be true? Also please recommend some references. Thanks a lot!

On a closed manifold $M$, let $P(f)=0$ be a linear overdetermined elliptic smooth PDE of 2nd order; for simplicity, let's assume it is for a real-valued function $f$. If a solution $f$ is zero on an open subset, then is $f$ zero on the whole of $M$? If this is not true in general, what would be conditions for it to be true? Also please recommend some references. Thanks a lot!

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user38064
user38064
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unique continuation property for overdetermined elliptic PDE

On a closed manifold M, let P(f)=0 be a linear overdetermined elliptic smooth PDE of 2nd order.(For simplicity, let's assume it is for a real-valued function f.) If a solution f is zero on an open subset, then is f zero on the whole M? If not in general, what would be conditions for it to be true? Also please recommend some references. Thanks a lot!