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PDE HW1

Chpater I PDEIntro

Chapter II Laplace

\(n\ge 3\) , \(f\in C_c^2(R^n)\),则 \(f*\Phi\) 有界 LaplaceQuestion Question

Chapter V 5.10 problems

1 Holder

2 Holderint

4 SobolevIneqn1

5 SobolevApprox

6 POU

11 Approx Corollary

12 \(\|D^hu\|_{L^1(V)}\le C \nRightarrow Du\)

13 反例

14 p=n

15 Poincare

17 Chain Rule

18 ChainRuleApply

\(\int u\phi = 0\ \Rightarrow\ u=0\text{ a.e. }\) RealAnalysisApprox

example

Sobolev Spaces Banach

embedded Corollary、 Bounded

GSI

compact embedded