- Turkish Journal of Mathematics
- Vol: 41 Issue: 3
- A two-obstacle problem with variable exponent and measure data
A two-obstacle problem with variable exponent and measure data
Authors : Hongtao Li, Xiaojuan Chai
Pages : 717-724
View : 6 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We consider a two-obstacle problem with measure data. For measures that do not charge sets of zero $p(\cdot)$-capacity, we obtain the existence and uniqueness of the solution. On the other hand, for the measure concentrated on a set with zero $p(\cdot)$-capacity, we prove a nonexistence result in the sense that when one looks for solutions via approximation, one cannot find a reasonable solution; see Theorem 2.3 and Remark 2.1 below.Keywords : Variable exponent, obstacle problems, measure data