논문KCI 등재
Elliptic equations with compactly supported solutions
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For any p ∈ (1, 2) and arbitrary f ∈ Lp(R2) with compactsupport, it is proved that there exists a pair (L, u), with L second orderuniformly elliptic operator and u ∈ W20 ,p(R2) such that Lu = f a.e. in R2.
Abstract
For any p ∈ (1, 2) and arbitrary f ∈ Lp(R2) with compactsupport, it is proved that there exists a pair (L, u), with L second orderuniformly elliptic operator and u ∈ W20 ,p(R2) such that Lu = f a.e. in R2.
참고문헌 (7)
- K. Astala, "Pucci’s conjecture and the Alexandrov inequality for elliptic PDEs in the plane", J. Reine Angew. Math, 591, pp.49~74 (2006)
- L. Bers, "Partial Differential Equations" (1964), Interscience
- P. Buonocore, "Solutions to two dimensional, uniformly elliptic equations, that lie in Sobolev spaces and have compact support", Rend. Circ. Mat. Palermo (2), 51(3), pp.476~484 (2002)
- C. Giannotti, "A compactly supported solution to a three-dimensional uniformly elliptic equation without zero order term", J. Differential Equations, 201(2), pp.234~249 (2004)
- C. Giannotti, "Expansions with Poisson kernels and related topics", Proc. Edinb. Math. Soc. (2), 53(1), pp.153~173 (2010)
- C. Giannotti, "On elliptic extensions in the disk", Potential Anal, 33(3), pp.249~262 (2010)
- T. H. Wolff, "Some constructions with solutions of variable coefficient elliptic equations", J. Geom. Anal, 3(5), pp.423~511 (1993)
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