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

2012/05/08 by Andrea Dall’Aglio, Dall'Aglio, Andrea, Alessio Porretta +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1205.1666

openalex publication_date 2012/05/08 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the regularity of weak solutions and subsolutions of\nsecond-order elliptic equations having a gradient term with superquadratic\ngrowth. We show that, under appropriate integrability conditions on the data,\nall weak subsolutions in a bounded and regular open set Om are\nH "older-continuous up to the boundary of Om. Some local and global\nsummability results are also presented. The main feature of this kind of\nproblems is that the gradient term, not the principal part of the operator, is\nresponsible for the regularity.\n

Citations

• Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side

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