List questions from sobolev-spaces

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Trace of $L^p$ function

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Show that it is a element of $(H^1(\Omega))'$

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Extension theorems in Sobolev spaces: Solving for constants

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Prove the function $u(x):=1-|x|^{2-N}$ is in $W^{2,p}$ on $\{x\in \mathbb R^N;\,\,|x|>1\}$

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Estimate in Sobolev Spaces

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Local Estimates for higher order homogeneous elliptic operators

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How can I complete my proof: Sobolev space W^(1,p) is complete? Using Convergence theorem

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Derivative of a function in the context of Sobolev spaces

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Use $C^\infty$ function to approximate $W^{1,\infty}$ function in finite domain

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Sobolev multiplication theorem

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Weak derivative as an $L^2$ limit of the difference quotient

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Evans PDE mappings into better spaces

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Equivalence discrete H^2 Sobolev norms

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Poincare inequality on arbitrary finite domain for the case that $\|u-u_\Omega\|_{L^q}\leq \|\nabla u\|_{L^q}$ where $1<q<p$

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List Question

Proving a Sobolev-Type inequality (also it is related to variational problem)

Trace of $L^p$ function

Show that it is a element of $(H^1(\Omega))'$

Extension theorems in Sobolev spaces: Solving for constants

Prove the function $u(x):=1-|x|^{2-N}$ is in $W^{2,p}$ on $\{x\in \mathbb R^N;\,\,|x|>1\}$

Estimate in Sobolev Spaces

Local Estimates for higher order homogeneous elliptic operators

How can I complete my proof: Sobolev space W^(1,p) is complete? Using Convergence theorem

Derivative of a function in the context of Sobolev spaces

Use $C^\infty$ function to approximate $W^{1,\infty}$ function in finite domain

Sobolev multiplication theorem

Weak derivative as an $L^2$ limit of the difference quotient

Evans PDE mappings into better spaces

Equivalence discrete H^2 Sobolev norms

Poincare inequality on arbitrary finite domain for the case that $\|u-u_\Omega\|_{L^q}\leq \|\nabla u\|_{L^q}$ where $1<q<p$

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