Hongtao LI, Xiaojuan CHAI

A two-obstacle problem with variable exponent and measure data

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

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.

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