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Results tagged with sobolev-spaces
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user 132487
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
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Does the function with the αth-weak partial derivative has the βth-weak partial derivative w...
The definition of weak derivative in the book Partial Differential Equations by Evans is stated as follows:
Suppose $u,v \in L_{loc}^1(U)$, and $\alpha$ is a multiindex. We say that $v$ is the $\a …
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While doing Lp estimates, is the constant C monotonically increasing with respect to the par...
For example, consider the third boundary value problem:
\begin{align}
&\frac{\partial u}{\partial t}-\sum_{i,j=1}^n a_{ij}(x,t) \frac{\partial^2 u}{\partial x_i \partial x_j} + \sum_{i=1}^n b_i(x, …
- 51