L1-Contraction and Uniqueness for Quasilinear Elliptic–Parabolic Equations

✍ Scribed by Felix Otto

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 565 KB
• Volume: 131
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0155

✦ Synopsis

We prove the L 1 -contraction principle and uniqueness of solutions for quasilinear elliptic parabolic equations of the form

where b is monotone nondecreasing and continuous. We assume only that u is a weak solution of finite energy. In particular, we do not suppose that the distributional derivative t [b(u)] is a bounded Borel measure or a locally integrable function.