Classical solutions for the system $\bf {\text{curl}\, v = g}$, with vanishing Dirichlet boundary conditions

Luigi C. Berselli; Placido Longo

doi:10.3934/dcdss.2019015

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2019, Volume 12, Issue 2: 215-229. Doi: 10.3934/dcdss.2019015

This issue Previous Article Navier-Stokes equations: Some questions related to the direction of the vorticity Next Article Fourth-order problems with Leray-Lions type operators in variable exponent spaces

Classical solutions for the system $\bf {\text{curl}\, v = g}$, with vanishing Dirichlet boundary conditions

Luigi C. Berselli^, and
Placido Longo

Dipartimento di Matematica, Università di Pisa, Via F. Buonarroti 1/c, Pisa, I-56127, Italy

* Corresponding author: Luigi C. Berselli
* Corresponding author: Luigi C. Berselli

Dedicated to Prof. Vicenţiu D. Rădulescu on the occasion of his 60 ^th birthday

Received: June 2017

Revised: November 2017

Published: April 2019

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Abstract

We consider the boundary value problem associated to the curl operator, with vanishing Dirichlet boundary conditions. We prove, under mild regularity of the data of the problem, existence of classical solutions.

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Mathematics Subject Classification: Primary: 26B12; Secondary: 35C05, 35F15.

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References

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