A priori bounds for weak solutions to elliptic equations with nonstandard growth

2011/02/08 by Patrick Winkert, Winkert, Patrick, Rico Zacher +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1102.1646

14 pages

openalex publication_date 2011/02/08 · arxiv created 2015/10/02 · arxiv updated 2015/10/05 · openalex created_date 2022/08/22 · openalex updated_date 2026/07/28

Abstract

In this paper we study elliptic equations with a nonlinear conormal derivative boundary condition involving nonstandard growth terms. By means of the localization method and De Giorgi's iteration technique we derive global a priori bounds for weak solutions of such problems.

Citations

• Mathematical modeling of electrorheological materials

Cited by

• Global boundedness of weak solutions with finite energy to a general class of Dirichlet problems
• Non-homogeneous conormal derivative problem for quasilinear elliptic equations with Morrey data

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