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Classical solution of PDE with mixed boundary conditions 
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#1
Feb2912, 09:21 AM

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Nowadays people usually consider PDEs in weak formulations only, so I have a hard time finding statements about the existence of classical solutions of the Poisson equation with mixed DirichletNeumann boundary conditions.
Maybe someone here can help me and point to a book or article where I can find sufficient conditions on the right hand side that guarantee the existence of a C^2 solution. 


#2
Mar112, 07:30 AM

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Thanks
PF Gold
P: 39,327

A google search on "DirichletNeumann conditions" turn up this:
http://www.math.osu.edu/~gerlach.1/m...t/node142.html 


#3
Mar112, 09:14 AM

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I did an extended Google search before I posed the question here, and found nothing useful. 


#4
Mar112, 02:34 PM

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Classical solution of PDE with mixed boundary conditions
There's a short section in Polyanin's handbook "Linear Partial Differential Equations" covering this case, but it does not appear to be available online. I'm not sure if the material there answers your question.



#5
Mar212, 11:41 AM

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#6
Mar912, 12:12 PM

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http://sharif.edu/~asghari/Handbook%...20Polyanin.pdf Section 7.2 is about the Poisson equation, but it concentrates on specific solutions for nice domains. No existence results. 


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