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 are Hölder-continuous up to the boundary of the set. 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. - See more at: http://www.ams.org/journals/tran/2015-367-05/S0002-9947-2015-05976-5/#sthash.WPapGnMK.dpuf
Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian / Dall'Aglio, Andrea; A., Porretta. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 367:5(2015), pp. 3017-3039. [10.1090/S0002-9947-2015-05976-5]
Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian
DALL'AGLIO, Andrea;
2015
Abstract
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 are Hölder-continuous up to the boundary of the set. 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. - See more at: http://www.ams.org/journals/tran/2015-367-05/S0002-9947-2015-05976-5/#sthash.WPapGnMK.dpuf| File | Dimensione | Formato | |
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