Question

If $u\in W_{0}^{1,p}(\Omega)\cap C(\Omega)$ and $N$ is a nodal domain of $u$ , then does it follow that $u\in W_{0}^{1,p}(N)$?

score 99 · Answer 1 · 2014-09-07 02:47:27

99

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If $u\in W_{0}^{1,p}(\Omega)\cap C(\Omega)$ and $N$ is a nodal domain of $u$ , then does it follow that $u\in W_{0}^{1,p}(N)$?

Published on 07 Sep 2014 - 2:47

score 2.1k · Answer 2 · 2014-09-07 17:34:31

2.1k

Views

Existence theorem on weak solutions of ordinary differential equations

Published on 07 Sep 2014 - 17:34

score 1.1k · Answer 3 · 2014-09-09 21:47:29

1.1k

Views

Approximating by smooth functions with compact support.

Published on 09 Sep 2014 - 21:47

score 108 · Answer 4 · 2014-09-10 00:39:44

108

Views

Constructing a function $u\in (W_0^{1,p}(B)\cap C(B))\setminus C(\overline{B})$.

Published on 10 Sep 2014 - 0:39

score 226 · Answer 5 · 2014-09-11 05:43:57

226

Views

An inequality using Sobolev norms

Published on 11 Sep 2014 - 5:43

score 33 · Answer 6 · 2014-09-11 05:55:07

33

Views

Associating a function $v \in H^{k+1}(K)$ with a polynomial function with equal integrals of derivatives

Published on 11 Sep 2014 - 5:55

score 249 · Answer 7 · 2014-09-11 16:57:13

249

Views

Product of weakly differentiable functions

Published on 11 Sep 2014 - 16:57

score 1.3k · Answer 8 · 2014-09-13 13:21:31

1.3k

Views

Is it true that $L^2$ is compactly embedded in $(W^{1,2}_{0})^{\ast}$?

Published on 13 Sep 2014 - 13:21

score 206 · Answer 9 · 2014-09-14 14:33:58

Is the sum of two Sobolev spaces defined on two different sets the Sobolev space defined on the union of these two sets?

score 477 · Answer 10 · 2014-09-16 19:06:12

477

Views

Two theorems about approximation by smooth functions

Published on 16 Sep 2014 - 19:06

score 1.6k · Answer 11 · 2014-09-16 21:34:37

1.6k

Views

Discrete Poincare Inequality

Published on 16 Sep 2014 - 21:34

score 668 · Answer 12 · 2014-09-17 15:17:17

668

Views

Traces of Sobolev functions in an unbounded domain

Published on 17 Sep 2014 - 15:17

score 74 · Answer 13 · 2014-09-17 16:36:39

74

Views

Closure of $C_0^{\infty}$ in $W^{k,p}(\Omega)$

Published on 17 Sep 2014 - 16:36

score 1.1k · Answer 14 · 2014-09-19 10:40:18

1.1k

Views

weak solution of poisson equation

Published on 19 Sep 2014 - 10:40

score 122 · Answer 15 · 2014-09-19 11:02:58

122

Views

$\left\|f\right\|_{L^{\infty}(\mathbb R^d)} \leq K \left\|f\right\|_{H^{s}(\mathbb R^d)}$

Published on 19 Sep 2014 - 11:02

List Question

If $u\in W_{0}^{1,p}(\Omega)\cap C(\Omega)$ and $N$ is a nodal domain of $u$ , then does it follow that $u\in W_{0}^{1,p}(N)$?

Existence theorem on weak solutions of ordinary differential equations

Approximating by smooth functions with compact support.

Constructing a function $u\in (W_0^{1,p}(B)\cap C(B))\setminus C(\overline{B})$.

An inequality using Sobolev norms

Associating a function $v \in H^{k+1}(K)$ with a polynomial function with equal integrals of derivatives

Product of weakly differentiable functions

Is it true that $L^2$ is compactly embedded in $(W^{1,2}_{0})^{\ast}$?

Is the sum of two Sobolev spaces defined on two different sets the Sobolev space defined on the union of these two sets?

Two theorems about approximation by smooth functions

Discrete Poincare Inequality

Traces of Sobolev functions in an unbounded domain

Closure of $C_0^{\infty}$ in $W^{k,p}(\Omega)$

weak solution of poisson equation

$\left\|f\right\|_{L^{\infty}(\mathbb R^d)} \leq K \left\|f\right\|_{H^{s}(\mathbb R^d)}$

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