[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2013.50.2.411

ELLIPTIC EQUATIONS WITH COMPACTLY SUPPORTED SOLUTIONS

Arena, Orazio (Dipartimento di Costruzioni e Restauro Universita di Firenze)
Giannotti, Cristina (Scuola di Scienze e Tecnologie Universita di Camerino)

Publication Information

Journal of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 411-423 More about this Journal

Abstract

For any $p{\in}(1,2)$ and arbitrary $f{\in}L^p(\mathbb{R}^2)$ with compact support, it is proved that there exists a pair (L, $u$ ), with L second order uniformly elliptic operator and $u{\in}W_0^{2,p}(\mathbb{R}^2)$ such that $Lu=f$ a.e. in $\mathbb{R}^2$ .

Keywords

second order elliptic equations; compactly supported solutions;

Citations & Related Records

Reference

1	C. Giannotti, A compactly supported solution to a three-dimensional uniformly elliptic equation without zero order term, J. Differential Equations 201 (2004), no. 2, 234-249. DOI ScienceOn
2	C. Giannotti and P. Manselli, Expansions with Poisson kernels and related topics, Proc. Edinb. Math. Soc. (2) 53 (2010), no. 1, 153-173. DOI ScienceOn
3	C. Giannotti and P. Manselli, On elliptic extensions in the disk, Potential Anal. 33 (2010), no. 3, 249-262. DOI
4	T. H. Wolff, Some constructions with solutions of variable coefficient elliptic equations, J. Geom. Anal. 3 (1993), no. 5, 423-511. DOI
5	L. Bers, F. John, and M. Schechter, Partial Differential Equations, Interscience, 1964.
6	P. Buonocore and P. Manselli, Solutions to two dimensional, uniformly elliptic equations, that lie in Sobolev spaces and have compact support, Rend. Circ. Mat. Palermo (2) 51 (2002), no. 3, 476-484. DOI
7	K. Astala, T. Iwaniec, and G. Martin, Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane, J. Reine Angew. Math. 591 (2006), 49-74.