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higher order parabolic equation; existence of solution; blow-up in finite time; higher order elliptic equation; variational method; strongly singular boundary value problem

References:

[1] Escudero, C., Gazzola, F., Peral, I.: **Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian**. J. Math. Pures Appl. (9) 103 (2015), 924-957. MR 3318175

[2] Escudero, C., Hakl, R., Peral, I., Torres, P. J.: **Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth**. Math. Methods Appl. Sci. 37 (2014), 793-807. DOI 10.1002/mma.2836 | MR 3188526

[3] Escudero, C., Hakl, R., Peral, I., Torres, P. J.: **On radial stationary solutions to a model of non-equilibrium growth**. Eur. J. Appl. Math. 24 (2013), 437-453. DOI 10.1017/S0956792512000484 | MR 3053654 | Zbl 1266.91051

[4] Escudero, C., Peral, I.: **Some fourth order nonlinear elliptic problems related to epitaxial growth**. J. Differ. Equations 254 (2013), 2515-2531. DOI 10.1016/j.jde.2012.12.012 | MR 3016212 | Zbl 1284.35435