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首页> 外文期刊>Infinite dimensional analysis, quantum probability, and related topics >Refined existence and regularity results for a class of semilinear dissipative SPDEs
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Refined existence and regularity results for a class of semilinear dissipative SPDEs

机译：一类半线性耗散SPDES的精致存在和规律性结果

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摘要

We prove the existence and uniqueness of solutions to a class of stochastic semilinear evolution equations with a monotone nonlinear drift term and multiplicative noise, considerably extending corresponding results obtained in previous work of ours. In particular, we assume the initial datum to be only measurable and we allow the diffusion coefficient to be locally Lipschitz-continuous. Moreover, we show, in a quantitative fashion, how the finiteness of the pth moment of solutions depends on the integrability of the initial datum, in the whole range p is an element of]0, infinity[. Lipschitz continuity of the solution map in pth moment is established, under a Lipschitz continuity assumption on the diffusion coefficient, in the even larger range p is an element of [0, infinity[. A key role is played by an Ito formula for the square of the norm in the variational setting for processes satisfying minimal integrability conditions, which yields pathwise continuity of solutions. Moreover, we show how the regularity of the initial datum and of the diffusion coefficient improves the regularity of the solution and, if applicable, of the invariant measures.
机译：我们证明了通过单调非线性漂移项和乘法噪声的一类随机半线性演化方程的存在性和唯一性，显着扩展了我们在我们的先前工作中获得的相应结果。特别是，我们假设仅可测量的初始数据，并且我们允许扩散系数是局部嘴唇连续的。此外，我们以定量方式展示了解决方案的第PH矩的有限度取决于初始数据的可积，在整个范围P是0，Infinity [。在第三矩的溶液映射的leipschitz连续性建立了在扩散系数上的Lipschitz连续性假设下，在甚至更大的范围P是[0，无限度的元素。通过ITO公式来播放关键作用，用于满足最小可积压条件的过程的变化设置中规范的正方形，从而产生了解决方案的方法。此外，我们展示了初始数据的规律性和扩散系数的规律如何提高解决方案的规律性，如果适用的不变措施。

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