Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian

Dall’Aglio, Andrea; Porretta, Alessio

doi:10.1090/S0002-9947-2015-05976-5

Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian
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Trans. Amer. Math. Soc. 367 (2015), 3017-3039 Request permission

Abstract:

In this paper, we study the regularity of weak solutions and subsolutions of second order elliptic equations having a gradient-dependent term with superquadratic growth. We show that, under appropriate integrability conditions on the data, all weak subsolutions in a bounded and regular open set $\Omega$ are Hölder-continuous up to the boundary of $\Omega$. Some local and global summability results are also presented. The main feature of this kind of problem is that the gradient term, not the principal part of the operator, is responsible for the regularity.

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