Identity $Delta u(x) = v´´(r) + frac{n-1}{r}v´(r)$ from a function
up vote
0
down vote
favorite
Let $Omega := {{x in mathbb{R}^n}:0 leq Vert xVert_2 < R}$ with $R> 0$.
Further, let $u in C^2(Omega)$ be a radial function.
How can one calculate/prove that this identity follows?
$$Delta u(x) = v´´(r) + frac{n-1}{r}v´(r)$$
I know that since $u in C^2(Omega)$ is a radial function it follows that there exists a function $v in C^2((0,R))$, so that $u(x) = v(r)$ for $x in Omega$, where $r := Vert x Vert_2$.
But I still can't follow the identity from this.
analysis functions norm
asked Nov 22 at 21:37
Math Dummy
83
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
Let $Omega := {{x in mathbb{R}^n}:0 leq Vert xVert_2 < R}$ with $R> 0$.
Further, let $u in C^2(Omega)$ be a radial function.
How can one calculate/prove that this identity follows?
$$Delta u(x) = v´´(r) + frac{n-1}{r}v´(r)$$
I know that since $u in C^2(Omega)$ is a radial function it follows that there exists a function $v in C^2((0,R))$, so that $u(x) = v(r)$ for $x in Omega$, where $r := Vert x Vert_2$.
But I still can't follow the identity from this.
analysis functions norm
asked Nov 22 at 21:37
Math Dummy
83
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $Omega := {{x in mathbb{R}^n}:0 leq Vert xVert_2 < R}$ with $R> 0$.
Further, let $u in C^2(Omega)$ be a radial function.
How can one calculate/prove that this identity follows?
$$Delta u(x) = v´´(r) + frac{n-1}{r}v´(r)$$
I know that since $u in C^2(Omega)$ is a radial function it follows that there exists a function $v in C^2((0,R))$, so that $u(x) = v(r)$ for $x in Omega$, where $r := Vert x Vert_2$.
But I still can't follow the identity from this.
analysis functions norm
asked Nov 22 at 21:37
Math Dummy
83
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let $Omega := {{x in mathbb{R}^n}:0 leq Vert xVert_2 < R}$ with $R> 0$.
Further, let $u in C^2(Omega)$ be a radial function.
How can one calculate/prove that this identity follows?
$$Delta u(x) = v´´(r) + frac{n-1}{r}v´(r)$$
I know that since $u in C^2(Omega)$ is a radial function it follows that there exists a function $v in C^2((0,R))$, so that $u(x) = v(r)$ for $x in Omega$, where $r := Vert x Vert_2$.
But I still can't follow the identity from this.
analysis functions norm
analysis functions norm
asked Nov 22 at 21:37
Math Dummy
83
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 22 at 21:37
Math Dummy
83
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 22 at 21:37
Math Dummy
83
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 22 at 21:37
Math Dummy
83
asked Nov 22 at 21:37
Math Dummy
83
83
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Math Dummy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Math Dummy is a new contributor. Be nice, and check out our Code of Conduct.
Math Dummy is a new contributor. Be nice, and check out our Code of Conduct.
Math Dummy is a new contributor. Be nice, and check out our Code of Conduct.
Math Dummy is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3009692%2fidentity-delta-ux-v%25c2%25b4%25c2%25b4r-fracn-1rv%25c2%25b4r-from-a-function%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
