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.
Quasiminimizers in one dimension: integrability of the derivate, inverse function and obstacle problems
SBORDONE, CARLO
2007-01-01
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.File in questo prodotto:
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