CAJ | 학술논문

考虑 p (x )-Laplace 方程 Dirichlet 边值问题的 L ∞估计，通过改进的迭代引理和De Giorgi 迭代，给出了非负不增函数 A k ∶=meas{x ∈Ω： u > k}的估计，并应用迭代引理得到了解的 L ∞正则性。结果表明：利用这种改进的 De Giorgi 迭代，在得到解的 L ∞估计时，也可得到该解对各种指标精确的依赖关系；这种正则性技术可应用到带有退化和奇异低阶项的偏微分方程中。
고필 p (x )-Laplace 방정 Dirichlet 변치문제적 L ∞고계，통과개진적질대인리화De Giorgi 질대，급출료비부불증함수 A k ∶=meas{x ∈Ω： u > k}적고계，병응용질대인리득도료해적 L ∞정칙성。결과표명：이용저충개진적 De Giorgi 질대，재득도해적 L ∞고계시，야가득도해해대각충지표정학적의뢰관계；저충정칙성기술가응용도대유퇴화화기이저계항적편미분방정중。
This paper is devoted to the maximum modulus estimation to the solution of a p (x)-Laplace equation with Dirichlet boundary condition.With the help of the modified iterative lemma,the author estimated the nonnegative non-increasing function A k ∶= meas{x ∈Ω: u > k}.As a result,the author obtained the L ∞ regularity by means of De Giorgi iteration technique.Using this technique one can obtain the accurate dependency of the solution on the index.On the other hand,this modified technique can be applied to some partial differential equations with degeneracy and singular lower order terms.