A Fully Nonlinear Boundary value Problem for the Laplace Equation in Dimension Two |
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Authors: | Rolando Magnanini |
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Institution: | Dipartimento di Matematica , Universita di Firenze , Italy |
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Abstract: | We study the regularity up to the boundary of solutions to the boundary value problem:math001] in D, ∣?u∣= g on &;pardD, where D is the unit disc. This problem finds its application in the study of geophysical and geomagnetic surveys. If g?C,math001](D) and is strictly positive, we prove that uis in the Holder class C1,α(D). An example shows that this is no longer true if g has some zeroes on ?D. In this case u isproved to be of class C1(D) |
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Keywords: | Nonlinear boundary value problem elliptic partial differential equations |
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