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Does this function live in $H^{\frac{1}{2}}(\partial \Omega)$

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#sobolev-spaces #trace #regularity-theory-of-pdes #poissons-equation #fractional-sobolev-spaces
182
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Regularity of higher order elliptic problem on compact smooth manifolds with boundary

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#smooth-manifolds #regularity-theory-of-pdes #manifolds-with-boundary #compact-manifolds #elliptic-operators
139
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Is Poisson formula valid for the weak solution of Laplacian?

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#real-analysis #calculus #partial-differential-equations #regularity-theory-of-pdes
110
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Regularity of solutions of heat eqaution with boundary conditions

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#partial-differential-equations #heat-equation #regularity-theory-of-pdes #smooth-functions #parabolic-pde
876
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What does the phrase "standard elliptic estimates" mean?

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#regularity-theory-of-pdes
137
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Gradient of fundamental solution of an elliptic PDE is also a solution far from the pole

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#partial-differential-equations #regularity-theory-of-pdes #elliptic-equations
182
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Estimate of supremum of a function by an integral

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#multivariable-calculus #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #fractional-sobolev-spaces
272
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elliptic PDE with discontinuous coefficients

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#partial-differential-equations #regularity-theory-of-pdes
58
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Parabolic equation with domain depending on time

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#partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
238
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Gradient estimate of degenerate parabolic equation

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#partial-differential-equations #reference-request #regularity-theory-of-pdes #parabolic-pde
35
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One question about regularity theory

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#partial-differential-equations #regularity-theory-of-pdes
80
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If $\int_{\Omega} [u_t + (f(u))_x ] \phi\, dt \,dx =0 $ for all $ \phi \in C_0^\infty$ ,then it's true for all $ \phi \in C_0$

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#partial-differential-equations #regularity-theory-of-pdes #greens-theorem
43
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Regularity for the critical case $p=2^*$

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#partial-differential-equations #regularity-theory-of-pdes
79
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Integral version of the lebesgue differentation theorem

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#integration #harmonic-analysis #regularity-theory-of-pdes
82
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References regularity of solutions to linear system of first order PDE

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#partial-differential-equations #reference-request #regularity-theory-of-pdes #linear-pde #parabolic-pde

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