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I have found many different and comprehensible proofs on the Internet for the uniqueness of the solution of the Poisson problem $$-Delta u=f quad texton $Omega subset mathbb R^n$, quad u=g quad texton $partial Omega$ $$
where $Omega subset mathbb R^n$ is some bounded domain provided that there does indeed exist a solution. However, I am having a hard time finding a full proof of the existence itself, can anyone either give me a proof or a link to the proof/relevant literature? Much appreciated.

pde poissons-equation

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asked Mar 13 at 19:13

TeslaTesla

887426

$endgroup$

add a comment | 

0

$begingroup$

I have found many different and comprehensible proofs on the Internet for the uniqueness of the solution of the Poisson problem $$-Delta u=f quad texton $Omega subset mathbb R^n$, quad u=g quad texton $partial Omega$ $$
where $Omega subset mathbb R^n$ is some bounded domain provided that there does indeed exist a solution. However, I am having a hard time finding a full proof of the existence itself, can anyone either give me a proof or a link to the proof/relevant literature? Much appreciated.

pde poissons-equation

share|cite|improve this question

asked Mar 13 at 19:13

TeslaTesla

887426

$endgroup$

add a comment | 

$begingroup$

I have found many different and comprehensible proofs on the Internet for the uniqueness of the solution of the Poisson problem $$-Delta u=f quad texton $Omega subset mathbb R^n$, quad u=g quad texton $partial Omega$ $$
where $Omega subset mathbb R^n$ is some bounded domain provided that there does indeed exist a solution. However, I am having a hard time finding a full proof of the existence itself, can anyone either give me a proof or a link to the proof/relevant literature? Much appreciated.

pde poissons-equation

share|cite|improve this question

asked Mar 13 at 19:13

TeslaTesla

887426

$endgroup$

share|cite|improve this question

asked Mar 13 at 19:13

TeslaTesla

887426

share|cite|improve this question

asked Mar 13 at 19:13

TeslaTesla

887426

asked Mar 13 at 19:13

TeslaTesla

887426

asked Mar 13 at 19:13

TeslaTesla

887426