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Does equality of (weak) gradients imply equality of functions up to a constant?

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#derivatives #partial-derivative #weak-derivatives
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Finding a function that satisfies certain integral conditions

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#inequality #integral-inequality #weak-derivatives
1.5k
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Intuition about weakly differentiable functions

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#weak-derivatives
189
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Weak Differentiability for the Absolute Value Function on the Unitball

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#functional-analysis #weak-derivatives
160
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Newton-Leibniz formula in $H^2((-1,1)\times (-1,1))$

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#real-analysis #sobolev-spaces #weak-derivatives
1.8k
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Weak form of Poisson-equation in 3D-cylindrical space (heat conduction)

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#weak-derivatives #poissons-equation #cylindrical-coordinates
84
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Sobolev spaces and weak derivatives. Meaning of $D^2$

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#sobolev-spaces #weak-derivatives
329
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$\theta$-Holder function and weak derivatives

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#functional-analysis #partial-differential-equations #banach-spaces #sobolev-spaces #weak-derivatives
434
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Definition of the weak solution to the Dirichlet boundary value problem

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#partial-differential-equations #sobolev-spaces #weak-derivatives #elliptic-equations
2.2k
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Is the composition of a Sobolev function and a smooth function Sobolev?

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#real-analysis #sobolev-spaces #regularity-theory-of-pdes #weak-derivatives
110
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Trace of Sobolev functions on a circle of radius R>0

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#functional-analysis #sobolev-spaces #trace #weak-derivatives
449
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How do I compute the weak derivative of this function?

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#functional-analysis #sobolev-spaces #weak-derivatives
136
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Raviart-Thomas elements for mixed u-p formulation

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#functional-analysis #sobolev-spaces #weak-derivatives #finite-element-method
311
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Higher differentiability of weak solutions to 2nd order elliptic PDEs with mixed boundary conditions

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#sobolev-spaces #regularity-theory-of-pdes #weak-derivatives #elliptic-equations
146
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Weak derivative Gronwall’s inequality

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#functional-analysis #weak-derivatives

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