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Intuition for regularity of solution of this hypoelliptic PDE

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#partial-differential-equations #regularity-theory-of-pdes #elliptic-equations #parabolic-pde
75
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Regularity estimate: $\|u\|_{H^{k+1}(\Omega)} \leq C\left(\|f\|_{H^{k-1}(\Omega)} + \|g\|_{H^{k+1/2}(\partial \Omega)} \right)$

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #fractional-sobolev-spaces
282
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Regularity of parabolic PDEs for large $\lambda$

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#reference-request #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #parabolic-pde
257
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PDE Fourier transformation method regularity of solution

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#partial-differential-equations #fourier-transform #regularity-theory-of-pdes
46
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$\displaystyle \min_{B} u \geq -\|\Delta u\|_{L^{2}}$

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#real-analysis #functional-analysis #partial-differential-equations #regularity-theory-of-pdes
13.6k
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Why should I "believe in" weak solutions to PDEs?

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#partial-differential-equations #soft-question #regularity-theory-of-pdes
101
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Is $e^{|x|^2}$ BMO?

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#real-analysis #functional-analysis #regularity-theory-of-pdes
176
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$L^2$ norm estimated by $H^{-2}$ norm.

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
243
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PDE Regularity Theory - Brezis

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
27
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boundary of zero level set (free boundary) of a p-harmonic function

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#real-analysis #analysis #partial-differential-equations #partial-derivative #regularity-theory-of-pdes
184
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Community-compiled errata for Bertozzi and Majda's "Vorticity and Incompressible Flow"?

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#partial-differential-equations #big-list #fluid-dynamics #regularity-theory-of-pdes
106
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Definition of a Subharmonic Function

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#functional-analysis #partial-differential-equations #calculus-of-variations #regularity-theory-of-pdes
128
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Density of subspaces of $L^2$

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#functional-analysis #sobolev-spaces #distribution-theory #regularity-theory-of-pdes
87
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A certain elliptic estimate I have trouble locating in books

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#regularity-theory-of-pdes #elliptic-equations
619
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Regularity of Laplace eigenfunctions up to the boundary

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#partial-differential-equations #eigenfunctions #regularity-theory-of-pdes #elliptic-equations

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