6533b820fe1ef96bd127a255
RESEARCH PRODUCT
The Obstacle Problem in a Non-Linear Potential Theory
P. Lehtolasubject
Harmonic functionObstacle problemMathematical analysisAxiomatic systemHarmonic (mathematics)Locally compact spaceType (model theory)Potential theoryAxiomMathematicsdescription
M. Brelot gave rise to the concept harmonic space when he extended classical potential theory on ℝn to an axiomatic system on a locally compact space. I have recently constructed1 a non-linear harmonic space by dropping the assumption that the sum of two harmonic functions is harmonic and considering some other axioms instead. This approach has its origin in the work of O. Martio, P. Lindqvist and S. Granlund2,3,4, who have developed a non-linear potential theory on ℝn connected with variational integrals of the type ∫ F(x,∇u(x)) dm(x), where F(x, h) ≈ |h|p.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1988-01-01 |