Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: Elliptic equations and systems

By Peter Poláčik, Pavol Quittner, Philippe Souplet. 2007

427 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/91634191ba96db1d7f545c48fc8704c55f09478d

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Liouville-type theorems and bounds of solutions of Hardy-Hénon equations (2012, background): “1 This reduction relies on two ingredients: (i) a change of variable, that allows to replace the coefficient |x|a with a smooth function which is bounded and bounded away from 0 in a suitable spatial domain; (ii) a generalization of a doubling-rescaling argument from [20] (see Lemma 2.”
Hamiltonian elliptic systems: a guide to variational frameworks (2014, background): “As for the reverse implication, suppose 4Except if N = 3 and 1 < p, q < 2∗ − 1, see for instance [80] for recent developments.”
Symmetry results for critical anisotropic p-Laplacian equations in convex cones (2019, background): “our setting. Note that, by convexity, there exists a constant LΣ >0 such that Σ is LΣ-Lipschitz. Then we let k0 >0 be the constant provided by Lemma 2.5 with L= LΣ. Lemma 2.7 (Doubling property [31]). Let ube a solution to (2.9), let LΣ be the Lipschitz constant of Σ, and let k0 >0 be the c”
Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy–Littlewood–Sobolev system of integral equations (2012, background): “The argument on the Lane–Emden conjecture can be seen in [20,22–25].”
On the fractional Lane-Emden equation (2014, result): “In the present work, we are interested in understanding whether similar results hold for equations involving a nonlocal diﬀusion operator, the simplest of which is perhaps the fractional laplacian.”
The L∞-Stokes semigroup in exterior domains (2012, background): “A blow-up argument is a typical indirect argument to obtain an a priori upper bound for solutions; see [23,26,39,40] (also [21]) for semilinear heat equations and [28,31] for the Navier–Stokes equations.”
Singularity and decay estimates in superlinear problems via liouville-type theorems. Part II: Parabolic equations (2007, methodology): “We note that our approach works for both elliptic and parabolic problems, and that the elliptic aspects have been developed in the preceding part [28].”