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How to calculate the first eigenvalue of laplace in $ \mathbb{R}_+^2 $?

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#functional-analysis #partial-differential-equations #eigenvalues-eigenvectors #elliptic-equations
69
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How to prove existence for semi-linear parabolic PDEs?

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#partial-differential-equations #elliptic-equations #nonlinear-analysis #parabolic-pde
113
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Confusion on a Remark regarding Unique Continuation

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#partial-differential-equations #elliptic-equations
58
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Trouble proving that an expression is a norm in $H^2(\mathbb{R}^N)$

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#functional-analysis #partial-differential-equations #sobolev-spaces #fourier-transform #elliptic-equations
546
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Calderón-Zygmund estimate for $\Omega=\mathbb{R}^N$

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#reference-request #sobolev-spaces #regularity-theory-of-pdes #elliptic-equations #singular-integrals
28
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Assume $u\in W^{k,p}(\Omega)$, does $u^q\in W^{k,p}(\Omega)$ for $q>0$?

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #elliptic-equations
122
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Hopf's Lemma's proof for subsolutions of Lu $\leq$ 0

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#analysis #partial-differential-equations #proof-explanation #maximum-principle #elliptic-equations
125
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Compactness of the trace operator of the Sobolev space

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#functional-analysis #partial-differential-equations #sobolev-spaces #elliptic-equations
133
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The sub-supersolution to solve an PDE

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#real-analysis #partial-differential-equations #elliptic-equations #variational-analysis
89
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Hyperbolic, parabolic and elliptic PDEs behavior relationship with Conic sections

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#partial-differential-equations #conic-sections #elliptic-equations #hyperbolic-equations #parabolic-pde
43
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Regularity for "general form" Monge-Ampère equation

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#partial-differential-equations #regularity-theory-of-pdes #elliptic-equations
38
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Elliptic equations and variational formulation

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#partial-differential-equations #elliptic-equations #partial-functions
61
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Find a bilinear form and a linear form

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#functional-analysis #partial-differential-equations #elliptic-equations
43
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Using a version of Ekeland variational principle to minimize a functional

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#calculus-of-variations #elliptic-equations #linear-pde #variational-analysis #elliptic-operators
103
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Degenerate elliptic PDE is uniformly elliptic in lower dimensional subspace

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#partial-differential-equations #regularity-theory-of-pdes #elliptic-equations

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