RENORMALIZED SOLUTION FOR NONLOCAL ELLIPTIC EQUATION WITH DATA IN L^1
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Abstract
Our purpose is to investigate the existence and the uniqueness of the non-negative renormalized solution for the nonlocal elliptic equation – which is the generalized case of the fractional Laplace equation, with the data in . The technique we apply in this paper is approximation methods, including two steps: proving the existence of a weak solution for the nonlocal elliptic equation with the truncated data , instead of (the truncated method); approximating the weak solution to get the renormalized solution. Moreover, we also use the Young measure technique, the integral by part formula, and the method related to the nonlocal operator and Sobolev’s spaces with non-integer order.
Keywords
existence, nonlocal elliptic equation, renormalized solutions, uniqueness
Article Details
References
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