We derive explicit expressions of the homogeneous solutions with constant sign in two dimensional cones for Pucci's extremal equations. As examples of possible applications, we obtain monotonicity formulas for all nonnegative supersolutions and necessary and sufficient explicit conditions for non-existence results of Liouville type.
Homogeneous solutions of extremal Pucci's equations in planar cones / Leoni, Fabiana. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 263:(2017), pp. 863-879. [10.1016/j.jde.2017.03.004]
Homogeneous solutions of extremal Pucci's equations in planar cones
LEONI, Fabiana
2017
Abstract
We derive explicit expressions of the homogeneous solutions with constant sign in two dimensional cones for Pucci's extremal equations. As examples of possible applications, we obtain monotonicity formulas for all nonnegative supersolutions and necessary and sufficient explicit conditions for non-existence results of Liouville type.File allegati a questo prodotto
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