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Charcteristic function not in a fractional Sobolev space

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#measure-theory #change-of-variable #fractional-sobolev-spaces
691
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Different norms for the $H^{1/2}$ sobolev spaces

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#partial-differential-equations #normed-spaces #sobolev-spaces #fractional-sobolev-spaces #trace-map
54
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Setting values of $ u$ in $H^{1/2}$ on a set of zero measure

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#fractional-sobolev-spaces #trace-map
986
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Fractional Sobolev Spaces $ W^{s,\infty}(\Omega)$ on a bounded domain

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#sobolev-spaces #fractional-sobolev-spaces
103
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About functions in fractional Sobolev spaces $W^{s,p}(\mathbb{R})$ and $\lim_{x\rightarrow a^{+}}\int_{a}^{x}\frac{f(y)}{(x-y)^{s}}dy=0$

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#real-analysis #functional-analysis #lp-spaces #holder-inequality #fractional-sobolev-spaces
34
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Equivalence of the two definitions of the fractional Sobolev spaces

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#functional-analysis #sobolev-spaces #fractional-sobolev-spaces
69
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Integrating the fractional Laplacian over $\Omega$

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#functional-equations #functional-inequalities #fractional-calculus #functional-calculus #fractional-sobolev-spaces
82
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Relation between the negative Laplacian operator and its square root

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#functional-analysis #operator-theory #sobolev-spaces #fractional-sobolev-spaces
86
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Fractional Sobolev space with zero boundary

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#analysis #partial-differential-equations #sobolev-spaces #fractional-sobolev-spaces
58
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Regularity of FEM a priori

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#regularity-theory-of-pdes #finite-element-method #fractional-sobolev-spaces
102
Views

Reference for extension operators on Sobolev spaces

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#reference-request #sobolev-spaces #fractional-sobolev-spaces #trace-map
40
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A product of a $H^1_0(\Omega)$ function with a function defined on $S^{N-1}$ is also in $H^1_0(\Omega)$.

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#functional-analysis #partial-differential-equations #sobolev-spaces #linear-pde #fractional-sobolev-spaces
108
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Continuity of the fractional Laplacian operator

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#functional-analysis #fractional-sobolev-spaces
24
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Singularity in the Fractional Laplacian definition

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#functional-analysis #fractional-sobolev-spaces
74
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Realization of the Fractional Laplacian Operator in $L^2(\Omega)$.

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#functional-analysis #fractional-sobolev-spaces

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