论文标题
具有负BESOV指数和线性生长解决方案的PDE
A pde with drift of negative Besov index and linear growth solutions
论文作者
论文摘要
本文研究了一类PDE，其系数为负空间，其溶液具有线性生长。我们显示了轻度和弱解决方案的存在和独特性，这些解决方案在这种情况下是等效的，并且有几个连续性结果。为此，我们引入了临时BESOV-H {Ö} lder型空间，以允许线性生长，并研究热半群对它们的作用。我们通过引入这些空间的特殊子类结束了论文，该空间具有可分开的有用属性。
This paper investigates a class of PDEs with coefficients in negative Besov spaces and whose solutions have linear growth. We show existence and uniqueness of mild and weak solutions, which are equivalent in this setting, and several continuity results. To this aim, we introduce ad-hoc Besov-H{ö}lder type spaces that allow for linear growth, and investigate the action of the heat semigroup on them. We conclude the paper by introducing a special subclass of these spaces which has the useful property to be separable.
