# A question about notation in PDE

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1. Jul 16, 2015

### BiGyElLoWhAt

I'm reading through one of my profs papers, or starting. Actually it's 2 of my old profs, one I had for linear and one I had for diff eq. My question is in Section 1 of this paper.

"We begin with an analysis of a second order quasilinear partial dif-ferential inequality for real valued functions of n real variables,
$\Delta u - B|u|^{\epsilon} \geq 0$"
where B and epsilon are constants, and B> 0 ; 0<epsilon<1

What does the delta represent? Is it something to the effect of $\sum_n \partial_{x_i}$? Similar to Del? If not what does this mean?

2. Jul 16, 2015

### BiGyElLoWhAt

-.-
Ok, another question, not too much farther down. What does $\mathbb{C}^{\alpha}$ where alpha is between 0 and 1 imply?
Starting to think this paper may be over my head, especially if we're dealing with partial complex dimensions.

3. Jul 16, 2015

### TeethWhitener

Δ is the Laplacian operator.

Look up "Holder space" on Wikipedia.

And that's about all the help I can offer. This paper is way over my head.

4. Jul 16, 2015

Thanks