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具有非强制性低阶项的p(x)-Laplace方程的重整化解

Renormalized solutions of p(x)-Laplace equations with an optional low order term

  • 摘要: 研究了有界域 \varOmega 上具有非强制性低阶项 p\left(x\right) -Laplace椭圆方程满足Dirichlet边界条件的重整化解的存在性,其中方程左端项 H 是低阶项,没有强制性,但满足某些增长条件,右端项 f\in L^1\left(\varOmega \right) 。运用变指数函数空间理论、截断函数和梯度估计等方法,证明上述 p\left(x\right) -Laplace方程重整化解的存在性。

     

    Abstract: In the report, the existence of the renormalized solutions of the Dirichlet boundary conditions, which can be satisfied by px)-Laplace elliptic equations with an optional low order term in bounded domains Ω, was studied. The low order term H was optional, and which satisfied certain growth conditions, the right end item f belonged to L1 data. The function space theory, the truncation functions, and the gradient estimation methods were used to prove the existence of the renormalization solutions for px)-Laplace equations.

     

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