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Norm equivalence between $H^1(D)$ and $H^1_0(D)$

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#functional-analysis #normed-spaces #sobolev-spaces
45
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The restriction of functions in $H^1(\mathbb{R}^n)$ to a bouded open set $\Omega$ are in $H^1_0(\Omega)$?

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#functional-analysis #measure-theory #partial-differential-equations #sobolev-spaces
129
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Embedding in Bochner space

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#real-analysis #functional-analysis #partial-differential-equations #sobolev-spaces
395
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Continuous functions in Sobolev spaces

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#real-analysis #functional-analysis #analysis #sobolev-spaces #trace-map
175
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Basis for L2 and Sobolev spaces

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#functional-analysis #sobolev-spaces #harmonic-analysis
77
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Functional derivatives and gradients on Sobolev spaces

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#functional-analysis #partial-differential-equations #sobolev-spaces
34
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A question involving the proof that the instanton function minimize the Sobolev constant

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#ordinary-differential-equations #partial-differential-equations #sobolev-spaces
42
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Composition of a compacted supported function with a Holder continuous function is a $H^1_0$ function.

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#functional-analysis #partial-differential-equations #sobolev-spaces #elliptic-equations #fractional-sobolev-spaces
85
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Weak derivative of restriction and restriction of weak derivative

Published on
#sobolev-spaces #weak-derivatives
73
Views

Fractional Sobolev norm of the modulus of a function

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#sobolev-spaces #fractional-sobolev-spaces
116
Views

Does weak convergence in $H^1_0(\Omega)$ imply weak convergence of the weak derivatives in $L^2(\Omega)$?

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#functional-analysis #partial-differential-equations #sobolev-spaces #weak-convergence
90
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Global approximation Theorem

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#partial-differential-equations #sobolev-spaces #weak-derivatives
39
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Cauchy Problem as Continuous Operator between Normed Spaces

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #parabolic-pde
39
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Existence of laplacian imply existence of all the terms in its sum?

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#partial-differential-equations #hilbert-spaces #sobolev-spaces #weak-derivatives
70
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Negative Sobolev space with respect to radon measure

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#real-analysis #measure-theory #sobolev-spaces

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