We prove a Liouville theorem for the following heat system whose nonlinearity has no gradient structure: where pq > 1, p β₯ 1, q β₯ 1, and | p -q| small. We then deduce a localization property and uniform L β estimates of blowup solutions of this system.
A gradient bound and a liouville theorem for nonlinear poisson equations
β Scribed by Luciano Modica
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 224 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0010-3640
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π SIMILAR VOLUMES
In this paper, we derive a Liouville type theorem on a complete Riemannian manifold without boundary and with nonnegative Ricci curvature for the equation \(\Delta u(x)+h(x) u(x)=0\), where the conditions \(\lim _{r \rightarrow x} r^{-1} \cdot \sup _{x \in B_{p}(r)}|\nabla h(x)|=0\) and \(h \geqslan
## 0 with r ) 0 and m ) 1, and show some applications of the theorem to the nonexistence problem of positive solutions of quasilinear equations. Basic models leading to such nonlinear equations are the degenerate Laplace equation and the steady-state porous medium equation.
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