108 citations · 419 across the 35 of their papers we have counts for
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On polyharmonic regularizations of Hessian equations: Variational methods
Carlos Escudero
This work is devoted to the study of the boundary value problem \begin{eqnarray}\nonumber (-1)^αΔ^αu = (-1)^k S_k[u] + λf, \qquad x &\in& Ω\subset \mathbb{R}^N, \\ \nonumber u = \p…
Existence results for a fourth order partial differential equation arising in condensed matter physics
Carlos Escudero, Filippo Gazzola, Robert Hakl +2
We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity…
Existence of radial solutions to biharmonic Hessian equations
Carlos Escudero, Pedro J. Torres
This work presents the construction of the existence theory of radial solutions to the elliptic equation \begin{equation}\nonumber Δ^2 u = (-1)^k S_k[u] + λf(x), \qquad x \in B_1(0…
Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian
Carlos Escudero, Filippo Gazzola, Ireneo Peral
We consider a partial differential equation that arises in the coarse-grained description of epitaxial growth processes. This is a parabolic equation whose evolution is governed by…