A two-obstacle problem with variable exponent and measure data | Zendy

Hongtao Li | Zendy; Xiaojuan Chai | Zendy

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A two-obstacle problem with variable exponent and measure data

Author(s) -

Hongtao Li,

Xiaojuan Chai

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1409-9

Subject(s) - mathematics , measure (data warehouse) , obstacle , exponent , obstacle problem , variable (mathematics) , mathematical analysis , data mining , computer science , linguistics , philosophy , boundary (topology) , political science , law

We consider a two-obstacle problem with measure data. For measures that do not charge sets of zero p(·)capacity, we obtain the existence and uniqueness of the solution. On the other hand, for the measure concentrated on a set with zero p(·)-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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