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Two theorems of N. Wiener for solutions of quasilinear elliptic equations

O. MartioP. Lindqvist

subject

General Mathematics010102 general mathematicsMathematical analysisHarmonic (mathematics)01 natural sciencesParabolic partial differential equationPoincaré–Steklov operator010101 applied mathematicsNonlinear systemElliptic partial differential equationHarmonic functionLinear differential equationFree boundary problem0101 mathematicsMathematics

description

Relatively little is known about boundary behavior of solutions of quasilinear elliptic partial differential equations as compared to that of harmonic functions. In this paper two results, which in the harmonic case are due to N. Wiener, are generalized to a nonlinear situation. Suppose that G is a bounded domain in R n. We consider functions u: G--~R which are free extremals of the variational integral

yearjournalcountryeditionlanguage
1985-01-01
10.1007/bf02392541http://projecteuclid.org/euclid.acta/1485890400