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A function in $W^{2,p}$ for $p>n/2$ is a.e. second differentiable

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#real-analysis #sobolev-spaces #regularity-theory-of-pdes
51
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Existence of solution to Laplace equation

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #linear-pde
113
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Example of a function in the weighted Morrey space

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#functional-analysis #analysis #harmonic-analysis #regularity-theory-of-pdes
202
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Physical interpretation of a singular pde

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#partial-differential-equations #regularity-theory-of-pdes #parabolic-pde #dispersive-pde
90
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Uniform boundedness of weak solution

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #parabolic-pde #fractional-sobolev-spaces
135
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About pseudo-differential operators

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#partial-differential-equations #regularity-theory-of-pdes #elliptic-operators #pseudo-differential-operators #fractional-sobolev-spaces
524
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How to show that the mild solution to this parabolic equation is also a classical solution?

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#real-analysis #functional-analysis #partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
292
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What does it really mean for a wave equation to be critical?

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#functional-analysis #partial-differential-equations #wave-equation #regularity-theory-of-pdes #dispersive-pde
462
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Sobolev embedding for the $L^q$ norm.

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#real-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #fractional-sobolev-spaces
181
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$u'\in L^{\infty}(0,T;L^{2}(U))\cap L^{2}(0,T;H_{0}^{1}(U))$ regularity in the semigroup approach

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes #semigroup-of-operators
49
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Splitting a PDE into two subdomains: Regularity conditions at the interface point(s)

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#partial-differential-equations #regularity-theory-of-pdes
76
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Approximation of an element in the dual of the Sobolev Space

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#functional-analysis #measure-theory #partial-differential-equations #harmonic-analysis #regularity-theory-of-pdes
949
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Function in H(curl) $\cap$ H(div), but not in H1

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#analysis #partial-differential-equations #examples-counterexamples #sobolev-spaces #regularity-theory-of-pdes
163
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$ L^p$ regularity for weak solutions of non homogeneous heat equation

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #parabolic-pde
86
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Regularity of linear pde with smooth coefficients

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#partial-differential-equations #regularity-theory-of-pdes #linear-pde

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