Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

"Counterexamples" to the harmonic Liouville theorem and harmonic functions with zero nontangential limits

100%

Bonilla A.

Colloquium Mathematicum

2000

tom 83

nr 2

155-160

We prove that, if μ>0, then there exists a linear manifold M of harmonic functions in $ℝ^N$ which is dense in the space of all harmonic functions in $ℝ^N$ and lim_{{‖x‖→∞} {x ∈ S}} ‖x‖^{μ}D^{α}v(x) = 0 for every v ∈ M and multi-index α, where S denotes any hyperplane strip. Moreover, every nonnull function in M is universal. In particular, if μ ≥ N+1, then every function v ∈ M satisfies ∫_H vdλ =0 for every (N-1)-dimensional hyperplane H, where λ denotes the (N-1)-dimensional Lebesgue measure. On the other hand, we prove that there exists a linear manifold M of harmonic functions in the unit ball 𝔹 of $ℝ^N$, which is dense in the space of all harmonic functions and each function in M has zero nontangential limit at every point of the boundary of 𝔹.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Bonilla A.

1 2000

Wyniki wyszukiwania

"Counterexamples" to the harmonic Liouville theorem and harmonic functions with zero nontangential limits