Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1409-9
Keywords
Variable exponent, obstacle problems, measure data
First Page
717
Last Page
724
Recommended Citation
LI, H, & CHAI, X (2017). A two-obstacle problem with variable exponent and measure data. Turkish Journal of Mathematics 41 (3): 717-724. https://doi.org/10.3906/mat-1409-9
