✦ LIBER ✦
Strong Stability Results for Solutions of Elliptic Equations with Power-like Lower Order Terms and Measure Data
✍ Scribed by Luigi Orsina; Alain Prignet
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 151 KB
- Volume
- 189
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
Let u n be the sequence of solutions of
where W is a bounded set in R N and f n is a sequence of functions which is strongly convergent to a function f in L 1 loc (W 0 K), with K a compact in W of zero r-capacity; no assumptions are made on the sequence f n on the set K. We prove that if a has growth of order p -1 with respect to Nu (p > 1), and if q > r(p -1)/(r -p), then u n converges to u, the solution of the same problem with datum f, thus extending to the nonlinear case a well-known result by H. Brezis.