Journals and Conference Proceedings
Permanent URI for this communityhttps://hdl.handle.net/10877/136
Academic publications and conference proceedings from members of the university community.
Browse
Browsing Journals and Conference Proceedings by Author "Acker, Andrew F."
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item A Free Boundary Problem for the p-Laplacian: Uniqueness, Convexity, and Successive Approximation of Solutions(Southwest Texas State University, Department of Mathematics, 1995-06-21) Acker, Andrew F.; Meyer, R.We prove convergence of a trial free boundary method to a classical solution of a Bernoulli-type free boundary problem for the p-Laplace equation, 1 < p < ∞. In addition, we prove the existence of a classical solution in N dimensions when p = 2 and, for 1 < p < ∞, results on uniqueness and starlikeness of the free boundary and continuous dependence on the fixed boundary and on the free boundary data. Finally, as an application of the trial free boundary method, we prove (also for 1 < p < ∞) that the free boundary is convex when the fixed boundary is convex.Item Qualitative Behavior of Axial-Symmetric Solutions of Elliptic Free Boundary Problems(Southwest Texas State University, Department of Mathematics, 1997-01-08) Acker, Andrew F.; Lancaster, KirkA general free boundary problem in R3 is investigated for axial-symmetric solutions and qualitative geometric properties of the free boundary are compared to those of the fixed boundary for the axial and radial directions. Counterexamples obtained previously by the first author show that our results cannot hold in the same generality as those for similar free boundary problems in R2.