BOUNDS AND REPRESENTATIONS OF SOLUTIONS OF PLANAR DIV-CURL PROBLEMS

作者：Auchmuty Giles^*

来源：Quarterly of Applied Mathematics, 2017, 75(3): 505-524.

DOI：10.1090/qam/1463

• Div-curl
• planar vector fields
• stream function
• potential representations
• harmonic fields

Estimates and representations of solutions of div-curl systems for planar vector fields are described. Potentials are used to represent solutions as the sum of fields that depend on the source terms and harmonic fields dependent on the boundary data. Sharp 2-norm (energy) bounds for the least energy solutions on bounded regions with Lipschitz boundary are found. Prescribed flux, tangential or mixed flux and tangential boundary conditions require different potentials. The harmonic fields are represented and estimated using Steklov eigenfunctions. Some regularity results are obtained.

• 出版日期2017-9