Differential and Integral Equations

Finite energy weak solutions to some Dirichlet problems with very singular drift

Lucio Boccardo

Abstract

In this paper, the boundary problems (1.1) and (3.1) are studied. The main results are the existence of a bounded weak solution of (1.1) under the minimal assumption (1.3) on $E$, and of the quasilinear problem (Hamilton-Jacobi equation) (3.1).

Article information

Source
Differential Integral Equations, Volume 32, Number 7/8 (2019), 409-422.

Dates
First available in Project Euclid: 2 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1556762423

Mathematical Reviews number (MathSciNet)
MR3945762

Citation

Boccardo, Lucio. Finite energy weak solutions to some Dirichlet problems with very singular drift. Differential Integral Equations 32 (2019), no. 7/8, 409--422. https://projecteuclid.org/euclid.die/1556762423