Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains

By Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers. 2010

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Citations in the corpus

A Hardy-Moser-Trudinger inequality (2010, background): “For the related higher order equations see also [18].”
Weighted integrability of polyharmonic functions (2012, methodology): “ted with a membrane, the bilaplacian ∆2 is associated with a plate. Thereis a sizeable literaturerelatedto the bilaplacian, and more generally the N-laplacian∆N; see, e.g., the books [4], [10], [12], [14], and the papers [11], [20], [21], [23], [1], [15], [32], [33]. We could also mention that the b”
On the existence of stationary solutions for higher-order p-Kirchhoff problems (2014, background): “For more standard polyharmonic problems we mention the recent monograph [11].”
EXISTENCE OF NONTRIVIAL SOLUTIONS TO POLYHARMONIC EQUATIONS WITH SUBCRITICAL AND CRITICAL EXPONENTIAL GROWTH (2012, unknown): “We first introduce the constant Λ2m,m which is defined by Λ2m,m (Ω) = inf Hm 0 (Ω)\{0} ‖u‖(2) ‖u‖22 be the first eigenvalue of the poly-Laplacian operator ∆ (see [19]).”
A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem (2013, methodology): “into this we get Z Sn−1 (p−1)|∆θw|2+(pJ1− n(n − 4) 2 )|∇θw|2+(pJ2− n2(n− 4)2 16 )w2 ≤ 0. If n+4 n−4 < p < pc(n), then p−1 > 0, pJ1− n(n−4) 2 > 0 and pJ2− n2(n−4)2 16 > 0 (cf. p. 338 in [18]), so w ≡ 0 and then u ≡ 0. For applications in Section 6, we record the form of E(R;0,u) for a ”
Eigenvalues of poly-harmonic operators on variable domains (2012, background): “ been much less investigated. However, a renewed general interest in higher order operators has been growing in the last decades as it appears in the extensive monograph by Gazzola, Grunau and Sweers [10] devoted to recent developments in the theory of poly-harmonic operators. As for domain perturba”
A few shape optimization results for a biharmonic Steklov problem (2015, background): “First of all we note that, by elliptic regularity theory, v 1 , . . . , v | F | ∈ H 4 (˜ φ (Ω)) (see [19, § 2.5]). have We set By standard calculus in normed spaces we have:”