List questions from regularity-theory-of-pdes

Published on 18 Jun 2015 - 9:29

238

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How to solve a simple differential equation in the way of weak solutions?

Published on 27 Mar 2026 - 14:02

88

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If $\partial\Omega\in C^{2+\alpha}$ and $-\Delta\Theta=f\text{ in }\Omega$ with $f\in C_0^\infty(\Omega)$, then $\Theta\in C^{2+\alpha}$

Published on 24 Jun 2015 - 19:33

185

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Unicity of solution for a parabolic problem?

Published on 25 Jun 2015 - 19:04

804

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Is $H^2(\Omega)\cap H_0^1(\Omega)$ compactly embedded on $H_0^1(\Omega)$?

Published on 30 Jun 2015 - 13:03

301

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Does smoothness imply boundedness? Evans PDE chapter 2 Problem 18

Published on 03 Jul 2015 - 14:43

208

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Regularity of compactly supported solutions to the divergence equation: $\nabla\cdot \mathbf{v}=g$.

Published on 03 Jul 2015 - 17:44

111

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{$\mathbb u$ $\in W^{2,2}(\Omega)$ , such that $u=0$ , $ \Delta u=0 $ on $\partial \Omega $} $\subseteq$ $W^{2,2}(\Omega) \cap W^{1,2}_0(\Omega)$

Published on 07 Jul 2015 - 13:45

155

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Regularity for non-homogenous elliptic PDE

Published on 27 Mar 2026 - 4:18

64

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Maximum principle of p-Laplacian operator

Published on 09 Jul 2015 - 9:34

220

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How can we show that $u$ as a weak solution has properties $u \in L^{\infty}(\Omega)$ , $ u>0 $

Published on 11 Jul 2015 - 12:09

68

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$\{v_n \} $ is bounded in $W_0^{1,q}$ for $ 1 \leq q < \frac{N}{N-1}$

Published on 11 Jul 2015 - 19:49

669

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Regularity of solutions to a transport equation

Published on 23 Feb 2026 - 22:50

63

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proof of existence of a solution with $ f \in L^1$

Published on 15 Jul 2015 - 21:10

280

Views

Maximum Principle for the PDE $\Delta u - a^2u=a^2$

Published on 26 Mar 2026 - 20:44

List Question

Is function $u$ nice when all $\Delta^k u$ are nice?

How to solve a simple differential equation in the way of weak solutions?

If $\partial\Omega\in C^{2+\alpha}$ and $-\Delta\Theta=f\text{ in }\Omega$ with $f\in C_0^\infty(\Omega)$, then $\Theta\in C^{2+\alpha}$

Unicity of solution for a parabolic problem?

Is $H^2(\Omega)\cap H_0^1(\Omega)$ compactly embedded on $H_0^1(\Omega)$?

Does smoothness imply boundedness? Evans PDE chapter 2 Problem 18

Regularity of compactly supported solutions to the divergence equation: $\nabla\cdot \mathbf{v}=g$.

{$\mathbb u$ $\in W^{2,2}(\Omega)$ , such that $u=0$ , $ \Delta u=0 $ on $\partial \Omega $} $\subseteq$ $W^{2,2}(\Omega) \cap W^{1,2}_0(\Omega)$

Regularity for non-homogenous elliptic PDE

Maximum principle of p-Laplacian operator

How can we show that $u$ as a weak solution has properties $u \in L^{\infty}(\Omega)$ , $ u>0 $

$\{v_n \} $ is bounded in $W_0^{1,q}$ for $ 1 \leq q < \frac{N}{N-1}$

Regularity of solutions to a transport equation

proof of existence of a solution with $ f \in L^1$

Maximum Principle for the PDE $\Delta u - a^2u=a^2$

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