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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
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