Singularity and decay estimates in superlinear problems via liouville-type theorems. Part II: Parabolic equations

By Peter Poláčik, Pavol Quittner, Philippe Souplet. 2007

202 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/60660517a422040a7710eadcef1bb9eedcf777d8

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations With Inverse Square Potentials (2014, methodology): “New results on universal estimates of spatial singularities for quasilinear elliptic equations of the form −∆mu = f(u) and also for semilinear systems of Lane–Emden type are obtained in [29] based on Liouville type theorems.”
A priori estimates for elliptic equations with reaction terms involving the function and its gradient (2018, unknown): “7] and there exists no ground state when |M | is small [23].”
A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem (2013, methodology): “By the doubling lemma [22], there exists another sequence yk ∈ B R0 , such that (1) M(yk)d(yk) 2k; (2) M(yk) M(xk); (3) M(z) 2M(yk) for any z ∈ B R0 such that |z − yk| k M(yk) .”
A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system (2010, methodology): “9) satisfying Dirichlet boundary conditions, we use a doubling lemma of Poláčik, Quittner and Souplet [21], the boundary Harnack inequality of Berestycki, Caffarelli and Nirenberg [3] and”
Partial regularity of finite Morse index solutions to the Lane–Emden equation (2011, background): “9 was proved in [17] for positive solutions, 1 < p < pS(N), and with a constant C independent of the Morse index m.”
A priori estimates and application to the symmetry of solutions for critical $p$-Laplace equations (2014, methodology): “The proof relies on rescaling arguments and a doubling property of Pol´aˇcik–Quittner–Souplet [22].”