List questions from maximum-principle

Published on 12 Nov 2021 - 11:05

69

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The modulus of a holomorphic function $f$ on a domain $D$ split into two subdomains $D_1$ and $D_2$.

Published on 20 Nov 2021 - 8:15

82

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How to prove that $|u(x)|\leq 1$ for all $x \in \Omega$, given u solves $-\vec \nabla^2 u = (1-u^2)\cdot u$ and $u=0$ on $\partial \Omega$.

Published on 21 Nov 2021 - 23:38

146

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Minimum value on the boundary of U help

Published on 22 Nov 2021 - 21:07

53

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maximum principle.. Proof check.

Published on 01 Dec 2021 - 14:56

123

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Proof of weak maximum principle for heat-type equations

Published on 01 Dec 2021 - 23:07

88

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A problem about using the moving plane method to prove radial symmetry of the $C^{2}$ global solution of a elliptic PDE in $R^{2}$

Published on 02 Dec 2021 - 14:13

126

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$f$ analytic in $\overline{\mathbb{D}}$ s.t $\int_{|z|=1}|f(z)-z||dz|\leq\frac{1}{100}$. Prove that $f$ has at least one zero in $\mathbb{D}$.

Published on 05 Dec 2021 - 18:56

154

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Heat Equation $u_{t} - \Delta u + u u_x + uu_y = 0$

Published on 08 Dec 2021 - 19:20

35

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Show that exist a function $u$ continuous in $\overline{\Omega}$

Published on 11 Dec 2021 - 17:42

66

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Optimal control problem with boundaries depending on control

Published on 11 Dec 2021 - 19:36

323

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Show that there exists a unique $z_0\in B(0,1)$ s.t $f(z_0)=z_0$.

Published on 25 Mar 2026 - 13:57

261

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Maximum principle question for heat equation problem

Published on 27 Mar 2026 - 8:46

117

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Does exist an holomorphic function $f$ on $|z|>1$, non-constant, and bounded by the limit at $\infty$?

Published on 18 Dec 2021 - 12:49

177

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Maximum principle for parabolic equation with mixed boundary condition

Published on 27 Mar 2026 - 8:44

List Question

Maximum principle for $-\Delta u=(u-1)(u+1)$

The modulus of a holomorphic function $f$ on a domain $D$ split into two subdomains $D_1$ and $D_2$.

How to prove that $|u(x)|\leq 1$ for all $x \in \Omega$, given u solves $-\vec \nabla^2 u = (1-u^2)\cdot u$ and $u=0$ on $\partial \Omega$.

Minimum value on the boundary of U help

maximum principle.. Proof check.

Proof of weak maximum principle for heat-type equations

A problem about using the moving plane method to prove radial symmetry of the $C^{2}$ global solution of a elliptic PDE in $R^{2}$

$f$ analytic in $\overline{\mathbb{D}}$ s.t $\int_{|z|=1}|f(z)-z||dz|\leq\frac{1}{100}$. Prove that $f$ has at least one zero in $\mathbb{D}$.

Heat Equation $u_{t} - \Delta u + u u_x + uu_y = 0$

Show that exist a function $u$ continuous in $\overline{\Omega}$

Optimal control problem with boundaries depending on control

Show that there exists a unique $z_0\in B(0,1)$ s.t $f(z_0)=z_0$.

Maximum principle question for heat equation problem

Does exist an holomorphic function $f$ on $|z|>1$, non-constant, and bounded by the limit at $\infty$?

Maximum principle for parabolic equation with mixed boundary condition

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