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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

1 vote

Elliptic regularity in $L^1$

I found a reference where elliptic equations in L1 are dealt with: Tanabe, "Functional analytical methods for partialdifferential equations" There it is also explained in what way the boundary values …
Richard Gustier's user avatar
4 votes
2 answers
809 views

Elliptic regularity in $L^1$

Dear all, I am looking for a good reference for elliptic regularity in $L^1$. To be more precise Let $\Omega\subset\mathrm{R}^n$ be a bounded smooth domain, let $A$ be a properly elliptic differenti …
Richard Gustier's user avatar
5 votes
3 answers
487 views

Continuity with values in L^2

Hi, let $T>0$, $\Omega\subset\mathrm{R}^n$ be a bounded smooth domain and suppose $$u\in L^2(0,T;W^{1,2}(\Omega))\cap L^\infty((0,T)\times\Omega))\ \text{and } \partial_tu\in L^2(0,T;W^{-1,2}(\Omega …
Richard Gustier's user avatar