Abstract
It is shown that a K-quasiminimizer u for the one-dimensional p-Dirichlet integral is a K′-quasiminimizer for the q-Dirichlet integral, 1 ≤ q < p 1(p, K), where p 1(p, K) > p; the exact value for p 1(p, K) is obtained. The inverse function of a non-constant u is also K′′-quasiminimizer for the s-Dirichlet integral and the range of the exponent s is specified. Connections between quasiminimizers, superminimizers and solutions to obstacle problems are studied.
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Martio, O., Sbordone, C. Quasiminimizers in one dimension: integrability of the derivative, inverse function and obstacle problems. Annali di Matematica 186, 579–590 (2007). https://doi.org/10.1007/s10231-006-0020-3
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DOI: https://doi.org/10.1007/s10231-006-0020-3