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Second variation corresponding to the functional

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#multivariable-calculus #sobolev-spaces #harmonic-functions #regularity-theory-of-pdes #fractional-sobolev-spaces
353
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Scaling the NS equation: supercriticality and energy estimate

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
72
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non-consistent initial conditions in finite volume method

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#partial-differential-equations #initial-value-problems #regularity-theory-of-pdes #finite-volume-method
117
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Smoothness of solution of parabolic type PDE

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#partial-differential-equations #regularity-theory-of-pdes
52
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Necessity of data smoothness for abstract parabolic IVP

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#functional-analysis #proof-verification #partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
146
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Is a Sobolev map with smooth minors smooth?

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#real-analysis #differential-geometry #sobolev-spaces #regularity-theory-of-pdes #jacobian
239
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A counter example for Liouville's theorem when the Jacobian is changing signs

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#sobolev-spaces #conformal-geometry #regularity-theory-of-pdes #jacobian #quasiconformal-maps
1.4k
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The interior gradient estimate for harmonic function

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#partial-differential-equations #regularity-theory-of-pdes
175
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Non-existence of weak solution in one dimension

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#analysis #partial-differential-equations #regularity-theory-of-pdes #linear-pde
1.6k
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Regularity of Parabolic pde

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#sobolev-spaces #regularity-theory-of-pdes #parabolic-pde
132
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$H^2$ regularity of weak solution for mixed Robin-Robin problem

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#partial-differential-equations #regularity-theory-of-pdes
274
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Best regularity for elliptic PDE with Neumann data

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #holder-spaces
95
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Higher regularity of weak solution for Laplace equation with Robin condition

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#regularity-theory-of-pdes #linear-pde
36
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When Sobolev maps are localizable?

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#differential-topology #riemannian-geometry #sobolev-spaces #regularity-theory-of-pdes
285
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Is being in the Sobolev space of power $\frac{d}{2}$ necessary for having well defined point evaluations?

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#functional-analysis #sobolev-spaces #regularity-theory-of-pdes #fractional-sobolev-spaces

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