The weak boundary effect in a field as a source approaches the boundary.
Krauklis, P.V., Krauklis, A.P. (2004)
Journal of Mathematical Sciences (New York)
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Krauklis, P.V., Krauklis, A.P. (2004)
Journal of Mathematical Sciences (New York)
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We study the composite membrane problem in all dimensions. We prove that the minimizing solutions exhibit a weak uniqueness property which under certain conditions can be turned into a full uniqueness result. Next we study the partial regularity of the solutions to the Euler–Lagrange equation associated to the composite problem and also the regularity of the free boundary for solutions to the Euler–Lagrange equations.