Calculus of Variations and Geometric Measure Theory
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A. Farina - J. Serrin

Entire solutions of completely coercive quasilinear elliptic equations, II

created by farina on 06 Jul 2010
modified on 16 Sep 2010


Accepted Paper

Inserted: 6 jul 2010
Last Updated: 16 sep 2010

Journal: Journal of Differential Equations
Year: 2010


In an earlier paper 3 the authors treated a broad class of quasilinear elliptic equations which have the property that any entire solution must necessarily be constant, a property of course not holding for the simple Laplace equation itself. Here we generalize the earlier class of equations to include cases where the "inhomogeneous terms" depend strongly on the gradient of the solution; see for example the model $p$-Laplace--type equation (2) below, as well as other more general examples discussed later.

Theorems 8 and 9 are particularly interesting in that, in contrast to the earlier conclusions, they require only the most minimal coercive behavior of the inhomogeneous terms when the solution variable lies in some arbitrarily large but bounded set; see especially the model example (15) at the end of the introduction.


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