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Dirichlet problems for fully anisotropic elliptic equations

Part of: Linear function spaces and their duals Elliptic equations and systems

Published online by Cambridge University Press:  04 November 2016

Giuseppina Barletta  and
Andrea Cianchi
Giuseppina Barletta
Affiliation:
Dipartimento di Ingegneria Civile, Energia, Ambiente e Materiali, Università Mediterranea di Reggio Calabria, Via Graziella – Loc. Feo di Vito, 89122 Reggio Calabria, Italy ([email protected])
Andrea Cianchi
Affiliation:
Dipartimento di Matematica e Informatica ‘U. Dini’, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy ([email protected])
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Extract

The existence of a non-trivial bounded solution to the Dirichlet problem is established for a class of nonlinear elliptic equations involving a fully anisotropic partial differential operator. The relevant operator depends on the gradient of the unknown through the differential of a general convex function. This function need not be radial, nor have a polynomial-type growth. Besides providing genuinely new conclusions, our result recovers and embraces, in a unified framework, several contributions in the existing literature, and augments them in various special instances.

Keywords

anisotropic elliptic equationsminimax methodscritical-point methodsanisotropic Orlicz–Sobolev spaces

MSC classification

Secondary: 35J20: Variational methods for second-order elliptic equations 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 1 , February 2017 , pp. 25 - 60
Copyright
Copyright © Royal Society of Edinburgh 2017 

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