Maximum principles for functionals associated with the solution of semilinear elliptic boundary value problems
โ Scribed by J. R. L. Webb
- Publisher
- Springer
- Year
- 1989
- Tongue
- English
- Weight
- 438 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0044-2275
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The paper addresses symmetry results for positive solutions of semilinear elliptic differential equations on a class of non-convex symmetrical domains. An example in two dimensions is the star of David. The moving plane method just shows that solutions coincide on three alternate corners of the star
We consider the boundary value problem =O, xE~(2, where f2 is a bounded region in ~" with smooth boundary Bu(x) = cth(x)u + (1 -ct)Ou/~n where c~ E [0, 1], h : ~I2 --~ ~+ with h = 1 when ~ = 1,)~ > 0,f is a smooth function such that f"(u) > 0 for u > O, f(u) < 0 for u E (0,fl) and f(u) > 0 for u > f