A Variation on the p(x)-Laplace Equation
نویسندگان
چکیده
For an elliptic equation with the p(x)-Laplacian, where exponent p(∙) is a bounded measurable function, we find conditions guaranteeing continuity of solution at point.
منابع مشابه
The Laplace Equation
Definition 1. Among the most important and ubiquitous of all partial differential equations is Laplace’s Equation: ∆u = 0, where the Laplacian operator ∆ acts on the function u : U → R (U is open in R) by taking the sum of the unmixed partial derivatives. For example: n = 1: ∆u = ∂ 2u ∂x2 = u = 0 In this simple case, the solution u = ax + b is found by integrating twice. n = 2: ∆u = ∂ 2u ∂x1 + ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-06205-z