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Compact Embedding Between Parabolic Holder Spaces

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#partial-differential-equations #regularity-theory-of-pdes #holder-spaces #parabolic-pde
48
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Solution of p-Laplace equation

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
270
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Equivalence of norms in the space $H_\Delta(\Omega)$

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#functional-analysis #partial-differential-equations #sobolev-spaces #laplacian #regularity-theory-of-pdes
191
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Inequality for the Laplace operator

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #linear-pde
164
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Solution of the non-linear Heat Equation

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#partial-differential-equations #regularity-theory-of-pdes #linear-pde #parabolic-pde #stochastic-pde
337
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Higher regularity for solutions of elliptic equations

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#regularity-theory-of-pdes #elliptic-equations
245
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Cut-off functions in Caccioppoli's inequality

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#regularity-theory-of-pdes
39
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Question on optimal regularity for the elliptic Neumann problem

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #elliptic-equations
131
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Estimate on average with weight

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#functional-analysis #analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
208
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Question on Sobolev extension onto boundary

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #trace-map
144
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How can a discontinuous function belong to $C_B^1(\Omega)$, the space of continuous functions $u$ with bounded derivatives?

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #continuity
97
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completion of $C^\infty_0(D)$ w.r.t $\|\cdot\|_\nabla$

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#sobolev-spaces #regularity-theory-of-pdes
80
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Distributional second-order derivatives of $\frac{e^{-|x|}}{4\pi |x|}$ to show the solution of $u -\Delta u=f$ is in $H^2$

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#partial-differential-equations #sobolev-spaces #distribution-theory #calculus-of-variations #regularity-theory-of-pdes
96
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estimating the gradient of a harmonic function on a ball

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#real-analysis #ordinary-differential-equations #partial-differential-equations #regularity-theory-of-pdes
382
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Subsolution of Laplace equation

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

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