Questions on "Partial Differential Equations", as opposed to "ordinary differential equations".

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3
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1answer
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+50

Biharmonic Equation in a Rectangle with Some Uncommon Boundary Conditions

Consider the following boundary value problem (BVP) $$\matrix{ {{\Delta ^2}H = 0,} \hfill & {} \hfill & {{\rm{in}}\,} \hfill & \Omega \hfill \cr {\partial _y^2H = 0} \hfill & ...
2
votes
0answers
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+100

Proving that if $f\in\mathcal{F}C^{1}_{b}(X)$ then $f\in W^{1,p}(X,\gamma$) for $p>1$

Let $X$ be a separable Banach space endowed with a centered nondegenerate Gaussian measure $\gamma$ and $H$ the Cameron-Martin space. Then consider $f\in\mathcal{F}C^{1}_{b}(X)$. I want to prove that ...
1
vote
1answer
20 views
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Where can i find references to proofs of 1D,2D (partially 3D) Navier Stokes Equation?

I'm currently trying to get into PDE's and as part of a course i'm focusing on proofs on existence of solutions to the Navier-Stokes Equations. Although existence of solutions has been proved for 1D ...