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Results tagged with sobolev-spaces
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user 55922
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
1
vote
A question about PDE argument involving monotone convergence theorem and Sobolev space
Hy
First: take $\varphi_n(t) w(x)$ where $\varphi(t)\in C_0([0,T))$ and $w\in H^1_0(\Omega)$. If $\varphi_n$ is well chosen and converges to the characteristic function of the set $[0,t]$ you will un …
- 121
1
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Getting existence for $L^1$ data given existence for $L^\infty$ data and $L^1$ continuous de...
Hy
First I have two remarks. The dependence continuous should be modified : it depends on $F(u_{01})-F(u_{02})$ and not on $u_{01}-u_{02}$. As far as the "weaker formulation" you do not precise the s …
- 121