How Long to Read Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three

How Long Does it Take to Read Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three?

It takes the average reader 1 hour and 23 minutes to read Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three by Robert C. Dalang

Assuming a reading speed of 250 words per minute. Learn more

Description

The authors study the sample path regularity of the solution of a stochastic wave equation in spatial dimension $d=3$. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any fixed $x\in\mathbb{R}^3$, the sample paths in time are Holder continuous functions. Further, the authors obtain joint Holder continuity in the time and space variables. Their results rely on a detailed analysis of properties of the stochastic integral used in the rigourous formulation of the s.p.d.e., as introduced by Dalang and Mueller (2003). Sharp results on one- and two-dimensional space and time increments of generalized Riesz potentials are a crucial ingredient in the analysis of the problem. For spatial covariances given by Riesz kernels, the authors show that the Holder exponents that they obtain are optimal.

How long is Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three?

Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three by Robert C. Dalang is 83 pages long, and a total of 20,999 words.

This makes it 28% the length of the average book. It also has 26% more words than the average book.

How Long Does it Take to Read Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three Aloud?

The average oral reading speed is 183 words per minute. This means it takes 1 hour and 54 minutes to read Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three aloud.

What Reading Level is Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three?

Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three?

Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three by Robert C. Dalang is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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