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Question on parabolic smoothing of nonhomogeneous heat equation

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #parabolic-pde
100
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Infinite differentiability for a solution of the general linear parabolic pde of second order

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#proof-explanation #regularity-theory-of-pdes #parabolic-pde
192
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Harnack inequality for linear parabolic equations

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#real-analysis #regularity-theory-of-pdes #parabolic-pde
102
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Norm estimate of $(-\lambda A+ I)^{-1}$ for strictly elliptic operator

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#functional-analysis #sobolev-spaces #regularity-theory-of-pdes
39
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Support of a regularized function

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#real-analysis #distribution-theory #regularity-theory-of-pdes
78
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Global elliptic regularity theory on $\mathbb{R}^n$ or interior estimates for elliptic pde when $p \neq 2$

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#reference-request #regularity-theory-of-pdes #elliptic-equations
250
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$\Delta u=3u$ then $u\equiv0$

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#real-analysis #functional-analysis #distribution-theory #regularity-theory-of-pdes
82
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weak convergence and compactness

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
108
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Elliptic regularity for $-\nabla \cdot(a(x)\nabla u)$

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes
770
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Weak solutions to $\Delta u=f$ are in $W^{2,2}$

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#real-analysis #functional-analysis #sobolev-spaces #regularity-theory-of-pdes
262
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Pointwise bound of the gradient of solutions of heat equations in the half-space.

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#real-analysis #multivariable-calculus #heat-equation #upper-lower-bounds #regularity-theory-of-pdes
454
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Easy to understand real world example for pde with only weak solutions

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#partial-differential-equations #examples-counterexamples #regularity-theory-of-pdes
302
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compute $H^{3/2}(\partial\Omega)$-norm for smooth $u$ and $\Omega$

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#sobolev-spaces #trace #regularity-theory-of-pdes #fractional-sobolev-spaces
220
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Greens function representation of nonlinear Poisson equation

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#partial-differential-equations #regularity-theory-of-pdes #greens-function #greens-theorem #linear-pde
102
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Regularity of Solution for the Kdv equation

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#partial-differential-equations #regularity-theory-of-pdes #nonlinear-analysis #linear-pde #dispersive-pde

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