Question

Measure of $\Omega_k = \{x\in \Omega\, : \, \operatorname{dist}(x,\partial \Omega)>\frac{1}{k}\}$, $\Omega$ is a bounded domain with smooth boundary

score 85 · Answer 1 · 2023-08-04 06:33:39

85

Views

Measure of $\Omega_k = \{x\in \Omega\, : \, \operatorname{dist}(x,\partial \Omega)>\frac{1}{k}\}$, $\Omega$ is a bounded domain with smooth boundary

Published on 04 Aug 2023 - 6:33

score 64 · Answer 2 · 2026-04-01 16:27:07

64

Views

Is $\|u\|_\infty\leq C\|u\|_{L^2}$ true for $u \in H^2(\mathbb{R}^{n})$ for $n>3$?

Published on 01 Apr 2026 - 16:27

score 35 · Answer 3 · 2023-08-06 16:50:47

35

Views

Continuation principle for a PDE

Published on 06 Aug 2023 - 16:50

score 84 · Answer 4 · 2026-03-26 14:22:34

84

Views

A detail in Evans's prove of THEOREM 3 in section 6.5 (about principal eigenvalue)

Published on 26 Mar 2026 - 14:22

score 74 · Answer 5 · 2023-08-07 13:57:13

74

Views

Does $\lVert D^2 u \rVert_p \leq C_p \Bigl( \lVert \Delta u \rVert_p +\lVert u \rVert_p \Bigr)$ hold for $u \in W^{2,p}$ in all $p \in [1,\infty)$?

Published on 07 Aug 2023 - 13:57

score 62 · Answer 6 · 2026-03-30 07:55:53

62

Views

Is $\sigma(-\Delta)=\sigma_{\mathrm{ess}}(-\Delta)$? Or under which conditions do we have this?

Published on 30 Mar 2026 - 7:55

score 86 · Answer 7 · 2023-08-08 16:55:23

86

Views

$\|u\|_{\infty}\leq C\|\Delta u\|_{L_2}+\|u\|_{L_2}$?

Published on 08 Aug 2023 - 16:55

score 33 · Answer 8 · 2023-08-11 07:18:37

33

Views

Estimates concerning difference quotients of Sobolev function

Published on 11 Aug 2023 - 7:18

score 23 · Answer 9 · 2023-08-11 14:36:09

23

Views

Well-posedness of weak formulation using SPUG method for advection-dominated equation

Published on 11 Aug 2023 - 14:36

score 21 · Answer 10 · 2023-08-11 15:55:28

21

Views

Does inverse inequality on spatial domain at least for smooth domain exist?

Published on 11 Aug 2023 - 15:55

score 51 · Answer 11 · 2026-03-25 07:46:06

51

Views

Is any homogeneous Sobolev space $\dot{W}^{s,p}$ a "homogeneous Banach space", as the the name suggests?

Published on 25 Mar 2026 - 7:46

score 69 · Answer 12 · 2023-08-12 11:51:38

69

Views

Continuous injection of Lipschitz space into $W^{1, \infty}$

Published on 12 Aug 2023 - 11:51

score 69 · Answer 13 · 2023-08-12 15:04:17

69

Views

Convergence of the integration of three functions

Published on 12 Aug 2023 - 15:04

score 79 · Answer 14 · 2023-08-14 12:16:42

79

Views

If $f \in L^2$ with weak derivative $\nabla f \in L^p$, do we have $f\in W^{1,p}$?

Published on 14 Aug 2023 - 12:16

score 19 · Answer 15 · 2026-03-28 16:14:08

19

Views

norm of space($V=H_{0}^{1}(U)\cap H^{2}(U)$)

Published on 28 Mar 2026 - 16:14

List Question

Measure of $\Omega_k = \{x\in \Omega\, : \, \operatorname{dist}(x,\partial \Omega)>\frac{1}{k}\}$, $\Omega$ is a bounded domain with smooth boundary

Is $\|u\|_\infty\leq C\|u\|_{L^2}$ true for $u \in H^2(\mathbb{R}^{n})$ for $n>3$?

Continuation principle for a PDE

A detail in Evans's prove of THEOREM 3 in section 6.5 (about principal eigenvalue)

Does $\lVert D^2 u \rVert_p \leq C_p \Bigl( \lVert \Delta u \rVert_p +\lVert u \rVert_p \Bigr)$ hold for $u \in W^{2,p}$ in all $p \in [1,\infty)$?

Is $\sigma(-\Delta)=\sigma_{\mathrm{ess}}(-\Delta)$? Or under which conditions do we have this?

$\|u\|_{\infty}\leq C\|\Delta u\|_{L_2}+\|u\|_{L_2}$?

Estimates concerning difference quotients of Sobolev function

Well-posedness of weak formulation using SPUG method for advection-dominated equation

Does inverse inequality on spatial domain at least for smooth domain exist?

Is any homogeneous Sobolev space $\dot{W}^{s,p}$ a "homogeneous Banach space", as the the name suggests?

Continuous injection of Lipschitz space into $W^{1, \infty}$

Convergence of the integration of three functions

If $f \in L^2$ with weak derivative $\nabla f \in L^p$, do we have $f\in W^{1,p}$?

norm of space($V=H_{0}^{1}(U)\cap H^{2}(U)$)

Trending Questions

Popular # Hahtags

Popular Questions