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Elliptic equations with nonstandard growth involving measures. (English) Zbl 1148.35034
The author prove the existence of a superharmonic function, which satisfies the equation $\operatorname{div} A(x,Du) = \mu$ in the sense of distributions. Here $$\mu$$ is a Radon measure and $$A$$ is an elliptic operator with $$p(x)$$-type nonstandard growth.

MSC:
 35J70 Degenerate elliptic equations 35D05 Existence of generalized solutions of PDE (MSC2000) 31C05 Harmonic, subharmonic, superharmonic functions on other spaces