bio | website | umpa.ens-lyon.fr/~serre |
---|---|---|
location | Lyon, FRANCE | |
age | 60 | |
visits | member for | 4 years, 8 months |
seen | 2 hours ago | |
stats | profile views | 11,252 |
My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2-volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. Benzoni-Gavage). I have edited in collaboration with S. Friedlander, a 4-volume Handbook of Mathematical Fluid Dynamics.
I have a continuous interest in Matrix Analysis. I have written a Graduate Text about Matrices. The second edition has been released in November 2010.
Apr 27 |
comment |
How has modern algebraic geometry affected other areas of math?
Sometimes, "I have a friend who ..." is the pretext for being allowed to say something one really thinks. I have in mind the famous aria Dites-lui, in La Grande-Duchesse de Gerolstein. Are you that friend ? |
Apr 22 |
revised |
Proofs of the uncountability of the reals.
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Apr 19 |
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When has the Borel-Cantelli heuristic been wrong?
If $n\ge2$, the argument gives $p=k2^{n+2}+1$. For this, use the fact that $2$ is a square imod $p$. This can be used to detect the first factor of $F_5$. It is a prime number of the form $k2^7+1$. But $k\ne1,3,4$ (not prime) $k\ne2$ (because another $F_m$ cannot be a factor). So the first candidate is $5\cdot128+1=641$, a factor found by Euler. |
Apr 15 |
awarded | Nice Answer |
Apr 10 |
revised |
Rigorous justification that overdetermined systems do not have a solution
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Apr 10 |
answered | Rigorous justification that overdetermined systems do not have a solution |
Apr 9 |
answered | Symmetric matrix from a nonsymmetricc matrix |
Mar 31 |
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“C^0 estimate for solutions to $\Delta(u)+e^{-u} \geq 0$”
This is not a special case. All the solutions $u$ are given by this formula, for a suitable holomorphic function $f$. |
Mar 31 |
revised |
“C^0 estimate for solutions to $\Delta(u)+e^{-u} \geq 0$”
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Mar 31 |
answered | “C^0 estimate for solutions to $\Delta(u)+e^{-u} \geq 0$” |
Mar 28 |
accepted | A “quadratic” triangular inequality |
Mar 27 |
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A “quadratic” triangular inequality
Thanks, Fedor ! |
Mar 27 |
revised |
A “quadratic” triangular inequality
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Mar 27 |
revised |
A “quadratic” triangular inequality
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Mar 27 |
revised |
A “quadratic” triangular inequality
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Mar 27 |
asked | A “quadratic” triangular inequality |
Mar 20 |
answered | Blow-Up for Semi-Linear Wave Equations |
Mar 12 |
awarded | Popular Question |
Mar 10 |
comment |
Density of smooth functions in Sobolev space, respecting nonnegative traces
Actually, a Theorem due to Stampacchia says that if $\phi$ is a Lipschit functin, then $u\mapsto\phi\circ u$ is a Lipschitz function from $W^{1,p}$ into itself. Apply this to $\phi(s)=s^+$. |
Mar 4 |
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Classification of PDE
@Qfwfq. Right, Schroedinger's equation is linear, but the number of independent variables is $1+3N$ where $N$ is the number of particles (electrons, protons, neutrons, ...) In practice, it is untractable by numerical schemes. For this reason, one makes approximations (density functional, Hartree-Fock, Slatter and so on), which replace it by a non-linear equation in $1+3$ variables. |