On absence of global positive solutions of elliptic inequalities with KPZ-nonlinearities

References

• Oleinik OA. On the equation Δu+k(x)eu=0. Russian Math Surveys. 1978;33(2):243–244. doi: 10.1070/RM1978v033n02ABEH002424
   Google Scholar
• Vekua IN. Some properties of solutions of Gauss's equation. Tr Mat Inst Steklova. 1961;64:5–8.
   Google Scholar
• Bitsadze AV. On the theory of a class of nonlinear partial differential equations. Differ Uravn. 1977;13(11):1993–2008.
   Google Scholar
• Kardar M, Parisi G, Zhang Y-C. Dynamic scaling of growing interfaces. Phys Rev Lett. 1986;56:889–892. doi: 10.1103/PhysRevLett.56.889
   PubMed Web of Science ®Google Scholar
• Medina E, Hwa T, Kardar M, et al. Burgers' equation with correlated noise: Renormalization group analysis and applications to directed polymers and interface growth. Phys Rev A. 1989;39:3053–3075. doi: 10.1103/PhysRevA.39.3053
   PubMed Web of Science ®Google Scholar
• Guedda M, Kersner R. Self-similar solutions to the generalized deterministic KPZ equation. Nonlinear Differ Equ Appl. 2003;10:1–13. doi: 10.1007/s00030-003-1036-z
   Web of Science ®Google Scholar
• Ginelli F, Hinrichsen H. Mean field theory for skewed height profiles in KPZ growth processes. J Phys A. 2004;37:11085–11100. doi: 10.1088/0305-4470/37/46/001
   Google Scholar
• Anh VV, Leonenko NN, Sakhno LM. Spectral properties of Burgers and KPZ turbulence. J Stat Phys. 2006;122:949–974. doi: 10.1007/s10955-005-9009-3
   Web of Science ®Google Scholar
• Spohn H. Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals. Phys A. 2006;369:71–99. doi: 10.1016/j.physa.2006.04.006
   Web of Science ®Google Scholar
• Gladkov A, Guedda M, Kersner R. A KPZ growth model with possibly unbounded data: correctness and blow-up. Nonlinear Anal. 2008;68:2079–2091. doi: 10.1016/j.na.2007.01.033
   Web of Science ®Google Scholar
• Benjamini I, Schramm O. KPZ in one dimensional random geometry of multiplicative cascades. Comm Math Phys. 2009;289:653–662. doi: 10.1007/s00220-009-0752-1
   Web of Science ®Google Scholar
• Duplantier B. Liouville quantum gravity and the KPZ relation: a rigorous perspective. In: Exner P, editor. Proceedings of the XVIth International Congress on Mathematical Physics; 2009 Aug 3–8; Prague, Czech Republic. Hackensack (NJ): World Scientific Publishing; 2010. p. 56–85.
   Google Scholar
• Quastel J. KPZ universality for KPZ. In: Exner P, editor. Proceedings of the XVIth International Congress on Mathematical Physics; 2009 Aug 3–8; Prague, Czech Republic. Hackensack (NJ): World Scientific Publishing; 2010. p. 401–405.
   Google Scholar
• Corwin I, Ferrari PL, Péché S. Universality of slow decorrelation in KPZ growth. Ann Inst Henri Poincaré Probab Stat. 2012;48:134–150. doi: 10.1214/11-AIHP440
   Web of Science ®Google Scholar
• Schehr G. Extremes of N vicious walkers for large N, application to the directed polymer and KPZ interfaces. J Stat Phys. 2012;149:385–410. doi: 10.1007/s10955-012-0593-8
   Web of Science ®Google Scholar
• Barral J, Jin X, Rhodes R, Vargas V. Gaussian multiplicative chaos and KPZ duality. Comm Math Phys. 2013;323:451–485. doi: 10.1007/s00220-013-1769-z
   Web of Science ®Google Scholar
• Spohn H. KPZ scaling theory and the semidiscrete directed polymer model. Math Sci Res Inst Publ. 2014;65:483–493.
   Google Scholar
• Bernardin C, Gonçalves P, Sethuraman S. Occupation times of long-range exclusion and connections to KPZ class exponents. Probab Theory Related Fields. 2016;166:365–428. doi: 10.1007/s00440-015-0661-5
   Web of Science ®Google Scholar
• Funaki T, Hoshino M. A coupled KPZ equation, its two types of approximations and existence of global solutions. J Funct Anal. 2017;273:1165–1204. doi: 10.1016/j.jfa.2017.05.002
   Web of Science ®Google Scholar
• Amann H, Crandall MG. On some existence theorems for semi-linear elliptic equations. Ind Univ Math J. 1978;27:779–790. doi: 10.1512/iumj.1978.27.27050
   Web of Science ®Google Scholar
• Kazdan JL, Kramer RJ. Invariant criteria for existence of solutions to second-order quasilinear elliptic equations. Comm Pure Appl Math. 1978;31:619–645. doi: 10.1002/cpa.3160310505
   Web of Science ®Google Scholar
• Pohožaev S. On equations of the form Δu=f(x,u,Du). Mat Sb. 1980;113:324–338.
   Google Scholar
• Mitidieri E, Pohožaev SI. A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities. Proc Steklov Inst Math. 2001;234:1–362.
   Google Scholar