论文标题
关于障碍问题的变异不平等的有效性，非标准生长
On the validity of variational inequalities for obstacle problems with non-standard growth
论文作者
论文摘要
本文的目的是表明，针对非标准生长条件的变异问题的解决方案满足了相应的变异不平等，而没有对生长和强制指数之间差距的任何微小假设。我们的结果依赖于基于凸分析的技术，包括建立双重公式和最小化器与相应的双最大化器之间的二重性公式，用于合适的近似问题，这些问题被保留到限制。在这方面，我们能够证明正确的竞争对手是具有有限能量的功能，与不受约束的结果一致。
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity exponents. Our results rely on techniques based on Convex Analysis that consist in establishing duality formulas and pointwise relations between minimizers and corresponding dual maximizers, for suitable approximating problems, that are preserved passing to the limit. In this respect we are able to show that the right class of competitors are the functions with finite energy, in agreement with the unconstrained results.
