A problem regerding Laplace operator in line integral
$begingroup$
$bigtriangleup = partial^2/partial x^2 + partial^2/partial y^2$ denote the Laplce operator.Let $omega ={(x,y)in $R$^2$$ :x^2+y^2<1}$ denote the boundary of domain $omega$. Consider the following boundary value problem.
$bigtriangleup u = c$ in $omega$ . $partial u/partial v =1$ on $partialomega$ . For what $c$ above problem has a solution.
MY OBSERVATION: I found thhis poblem on a textbook which gives a hint too!
By Green's theorem $$int_ omegabigtriangleup u dx dy = int_ { partialomega} partial u/partial n ds$$
$cpi = 2pi$ $implies c=2pi$.
We know in Green's line itegral equal surface integral; but WHY THEY USE LAPLACE OPERATOR IN LINE INTEGRAL? Thanks for reading
laplacian
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
$endgroup$
add a comment |
$begingroup$
$bigtriangleup = partial^2/partial x^2 + partial^2/partial y^2$ denote the Laplce operator.Let $omega ={(x,y)in $R$^2$$ :x^2+y^2<1}$ denote the boundary of domain $omega$. Consider the following boundary value problem.
$bigtriangleup u = c$ in $omega$ . $partial u/partial v =1$ on $partialomega$ . For what $c$ above problem has a solution.
MY OBSERVATION: I found thhis poblem on a textbook which gives a hint too!
By Green's theorem $$int_ omegabigtriangleup u dx dy = int_ { partialomega} partial u/partial n ds$$
$cpi = 2pi$ $implies c=2pi$.
We know in Green's line itegral equal surface integral; but WHY THEY USE LAPLACE OPERATOR IN LINE INTEGRAL? Thanks for reading
laplacian
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
$endgroup$
add a comment |
$begingroup$
$bigtriangleup = partial^2/partial x^2 + partial^2/partial y^2$ denote the Laplce operator.Let $omega ={(x,y)in $R$^2$$ :x^2+y^2<1}$ denote the boundary of domain $omega$. Consider the following boundary value problem.
$bigtriangleup u = c$ in $omega$ . $partial u/partial v =1$ on $partialomega$ . For what $c$ above problem has a solution.
MY OBSERVATION: I found thhis poblem on a textbook which gives a hint too!
By Green's theorem $$int_ omegabigtriangleup u dx dy = int_ { partialomega} partial u/partial n ds$$
$cpi = 2pi$ $implies c=2pi$.
We know in Green's line itegral equal surface integral; but WHY THEY USE LAPLACE OPERATOR IN LINE INTEGRAL? Thanks for reading
laplacian
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
$endgroup$
$bigtriangleup = partial^2/partial x^2 + partial^2/partial y^2$ denote the Laplce operator.Let $omega ={(x,y)in $R$^2$$ :x^2+y^2<1}$ denote the boundary of domain $omega$. Consider the following boundary value problem.
$bigtriangleup u = c$ in $omega$ . $partial u/partial v =1$ on $partialomega$ . For what $c$ above problem has a solution.
MY OBSERVATION: I found thhis poblem on a textbook which gives a hint too!
By Green's theorem $$int_ omegabigtriangleup u dx dy = int_ { partialomega} partial u/partial n ds$$
$cpi = 2pi$ $implies c=2pi$.
We know in Green's line itegral equal surface integral; but WHY THEY USE LAPLACE OPERATOR IN LINE INTEGRAL? Thanks for reading
laplacian
laplacian
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
asked Jan 14 at 15:13
Subhajit SahaSubhajit Saha
255113
255113
add a comment |
add a comment |
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