Can you be a bit more precise and descriptive?What does the colon notation, :, mean when it is inside an integral for weak solutions?
Apologies for the confusion, is it correct to say that $$\mathbf{x}\otimes\mathbf{x}:y$$ is equivalent notation for $$\langle\mathbf{x}\otimes\mathbf{x}, y\rangle$$ where the latter denotes the inner product. Perhaps, this question was more elementary than I had meant...Can you be a bit more precise and descriptive?
Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$I haven't seen the first one, and the second one calls for the question, what are you multiplying there?
If I build the ##\mathbf{x} \otimes \mathbf{x}## from this, I get a rank one ##3\times 3## matrix. How can this be multiplied by an ##y## via an inner product, wherever this is from?Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$