Uniqueness of solutions of a certain nonlinear elliptic equation on Riemannian manifolds
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In this paper, we prove that if every bounded $\mathcal A$-harmonic function on a complete Riemannian manifold $M$ is asymptotically constant at infinity of $p$-nonparabolic ends of $M$, then each bounded $\mathcal A$-harmonic function is uniquely determined by the values at infinity of $p$-nonparabolic ends of $M$, where $\mathcal A$ is a nonlinear elliptic operator of type $p$ on $M$. Furthermore, in this case, every bounded $\mathcal A$-harmonic function on $M$ has finite energy.
Abstract
In this paper, we prove that if every bounded $\mathcal A$-harmonic function on a complete Riemannian manifold $M$ is asymptotically constant at infinity of $p$-nonparabolic ends of $M$, then each bounded $\mathcal A$-harmonic function is uniquely determined by the values at infinity of $p$-nonparabolic ends of $M$, where $\mathcal A$ is a nonlinear elliptic operator of type $p$ on $M$. Furthermore, in this case, every bounded $\mathcal A$-harmonic function on $M$ has finite energy.
참고문헌 (17)
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