# 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)
• Published : 2013.03.01
• 83 3

#### 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

#### References

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