The Agmon-Miranda maximum principle for the polyharmonic equations of all orders is shown to hold in Lipschitz domains in ℝ3. In ℝn, n≥4, the Agmon-Miranda maximum principle and Lp-Dirichlet estimates for certain p>2 are shown to fail in Lipschitz domains for these equations. In particular if 4≤n≤2 m+1 the Lp Dirichlet problem for Δm fails to be solvable for p>2(n−1)/(n−3).
|Original language||English (US)|
|Number of pages||22|
|Journal||Potential Analysis: An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis|
|State||Published - Dec 1995|
- dilation invariant
- implicit functional
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