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Bilinear improvement at critical Sobolev regularity

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#real-analysis #functional-analysis #sobolev-spaces
587
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Functions that don't have a weak derivative in $L^p(\mathbb{R}^n)$

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#functional-analysis #partial-differential-equations #examples-counterexamples #sobolev-spaces #weak-derivatives
37
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A question about Sobolev functions

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#real-analysis #sequences-and-series #functional-analysis #sobolev-spaces
139
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Poincaré inequality and Lax-Milgram lemma on a convex space

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#functional-analysis #convex-analysis #sobolev-spaces #elliptic-equations #elliptic-operators
67
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Question from the inequality

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#partial-differential-equations #sobolev-spaces
102
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How do I prove the estimates?

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#partial-differential-equations #sobolev-spaces
70
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Is a locally invertible weak limit of injective maps injective almost everywhere?

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#real-analysis #differential-topology #sobolev-spaces #weak-convergence #geometric-measure-theory
69
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$H_1$ seminorm of an error in 2-D

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#partial-differential-equations #numerical-methods #normed-spaces #sobolev-spaces #finite-element-method
41
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Are Lipchitz isometries smooth up to the boundary?

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#riemannian-geometry #sobolev-spaces #isometry #regularity-theory-of-pdes #manifolds-with-boundary
317
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Proving that a functional J satisfies the Palais Smale condition

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#partial-differential-equations #sobolev-spaces #calculus-of-variations #boundary-value-problem #elliptic-equations
42
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Decompositing Sobolev Norms on Subspaces

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#real-analysis #functional-analysis #partial-differential-equations #solution-verification #sobolev-spaces
126
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What is the space $D^{k,p}$, and why Sobolev's embedding holds?

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#real-analysis #sobolev-spaces
44
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Computing using holder's and young's inequality

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#partial-differential-equations #lebesgue-integral #sobolev-spaces #holder-inequality #young-inequality
167
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Star-shaped domain and approximation by smooth functions

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#partial-differential-equations #sobolev-spaces
1k
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Prove that $u(x)=\log\log\left(1+\frac{1}{\vert x\vert}\right)\in H^1(B(0,1))$

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#real-analysis #functional-analysis #solution-verification #sobolev-spaces

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