List questions from regularity-theory-of-pdes

Published on 26 Mar 2026 - 18:41

103

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To get a strong convergent subsequence in $L^p_{loc}(\Omega)$ where $\Omega\subset\mathbb{R}^N$ is a smooth bounded domain and $1<,p<\infty.$

Published on 01 Jan 2018 - 6:10

260

Views

Regularity of a function

Published on 04 Jan 2018 - 1:35

32

Views

Smoothness on every compact $V\subset U$ implies smoothness on $U$?

Published on 09 Jan 2018 - 14:47

3.7k

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viscosity solution vs. weak solution

Published on 22 Mar 2026 - 9:46

85

Views

$H^1$-conforming approximation for elliptic PDE with discontinuous coefficient?

Published on 28 Mar 2026 - 6:06

112

Views

If $u \in H_0^1(\Omega) \cap L^p(\Omega)$ and $\Delta u \in L^p(\Omega)$ then $u \in W^{2, p}(\Omega)$

Published on 03 Aug 2020 - 19:17

542

Views

Weak maximum principle of strictly elliptic equation with solution in Sobolev space ( Gilberg Trudiger theorem 8.1)

Published on 06 Aug 2020 - 12:40

87

Views

Uniformly sectorial family: Differentiability of Resolvent

Published on 12 Aug 2020 - 12:45

46

Views

Establish conditions on initial data of the following first order PDE ( characteristics method)

Published on 27 Mar 2026 - 12:34

437

Views

Doubt about the proof of Moser Iteration in Gilbarg & Trudinger's book

Published on 28 Mar 2026 - 4:35

395

Views

On regularity of Hyperbolic Equations

Published on 28 Mar 2026 - 0:27

143

Views

Resource for $L^p$ regularity

Published on 28 Mar 2026 - 6:30

117

Views

Implicit Function Theorem for System of PDEs

Published on 29 Mar 2026 - 14:27

76

Views

Regularity of biharmonic problem with solution $u \in H_0^2(\Omega)$

Published on 27 Mar 2026 - 21:20

List Question

In what function space is the fractional Laplacian $(-\Delta)^su$ essentially bounded?

To get a strong convergent subsequence in $L^p_{loc}(\Omega)$ where $\Omega\subset\mathbb{R}^N$ is a smooth bounded domain and $1<,p<\infty.$

Regularity of a function

Smoothness on every compact $V\subset U$ implies smoothness on $U$?

viscosity solution vs. weak solution

$H^1$-conforming approximation for elliptic PDE with discontinuous coefficient?

If $u \in H_0^1(\Omega) \cap L^p(\Omega)$ and $\Delta u \in L^p(\Omega)$ then $u \in W^{2, p}(\Omega)$

Weak maximum principle of strictly elliptic equation with solution in Sobolev space ( Gilberg Trudiger theorem 8.1)

Uniformly sectorial family: Differentiability of Resolvent

Establish conditions on initial data of the following first order PDE ( characteristics method)

Doubt about the proof of Moser Iteration in Gilbarg & Trudinger's book

On regularity of Hyperbolic Equations

Resource for $L^p$ regularity

Implicit Function Theorem for System of PDEs

Regularity of biharmonic problem with solution $u \in H_0^2(\Omega)$

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