Timeline for An acting condition for a superposition operator from $H^1(\Omega)$ to $H^1(\Omega)$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 27, 2016 at 20:04 | comment | added | Jean Duchon | Apply the chain rule; $\nabla(f\circ v)=f'(v)\nabla v$. | |
| Dec 27, 2016 at 19:49 | comment | added | Vrouvrou | I man how we see that we must choose this condition | |
| Dec 27, 2016 at 17:22 | comment | added | Jean Duchon | Lipschitz continuity: $\sup_{s<t}|\frac{f(s)-f(t)}{s-t}|<\infty$ | |
| Dec 27, 2016 at 17:14 | comment | added | Vrouvrou | and how we find that $f'\in L^{\infty}$ please | |
| Dec 27, 2016 at 17:11 | comment | added | Jean Duchon | No, Bazin is right: for polynomials, only affine functions (polynomials of degree 1) work for $N\ge2$. | |
| Dec 27, 2016 at 17:06 | history | edited | Jean Duchon | CC BY-SA 3.0 |
correction
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| Dec 27, 2016 at 16:47 | comment | added | Vrouvrou | this answer is on contradiction with the answer of @Bazin no? | |
| Dec 27, 2016 at 16:41 | history | answered | Jean Duchon | CC BY-SA 3.0 |