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Weak solution of Laplace equation in $H^2$

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
56
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Show $u \notin H^2$ for $-\text{div}(a\Delta u)=1 $ where $a$ is a step function

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
46
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An estimate of integral

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#integration #functional-analysis #analysis #regularity-theory-of-pdes
97
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$\nabla div(B)=curl(E) \implies div(B)=0$ on non-convex domains

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes
38
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Homology group for critical points

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#functional-analysis #partial-differential-equations #algebraic-topology #regularity-theory-of-pdes
48
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What properties of $A:H^{-1/2}([0,2\pi])\to H^{1/2}([0,2\pi])$ allow us to bound the Sobolev operator norm of $A$ by the $L^2$ operator norm?

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#partial-differential-equations #fourier-analysis #operator-theory #sobolev-spaces #regularity-theory-of-pdes
49
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Elements in fractional Sobolev space

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#sobolev-spaces #regularity-theory-of-pdes #parabolic-pde #fractional-sobolev-spaces
227
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Poisson PDE solution regularity

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#regularity-theory-of-pdes #poissons-equation
502
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What is the Intersection between $H^2$ and $H^1_0$?

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#functional-analysis #sobolev-spaces #regularity-theory-of-pdes #finite-element-method
40
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Well definedness of the p fractional Laplace operator

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#integration #analysis #partial-differential-equations #regularity-theory-of-pdes #fractional-sobolev-spaces
56
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Special Case for "Interior Regularity"

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#partial-differential-equations #calculus-of-variations #regularity-theory-of-pdes
151
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Fractional Sobolev space

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#partial-differential-equations #regularity-theory-of-pdes #parabolic-pde #fractional-sobolev-spaces
401
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Financial importance of the diffusion term in Black-Scholes partial differential equation

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#numerical-methods #finance #regularity-theory-of-pdes #parabolic-pde
114
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Supremum of an integral

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#real-analysis #analysis #partial-differential-equations #regularity-theory-of-pdes
199
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An integral estimate regarding tails of solutions in Di Castro–Kuusi–Palatucci

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#integration #analysis #partial-differential-equations #regularity-theory-of-pdes #parabolic-pde

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