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Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

1 vote
0 answers
37 views

Regularity of a flux induced by a potential

Take $\Omega\subset R^n$ with smooth boundary (take a ball for example) a function $f\in L^{\infty}(\Omega)$ with support strictly contained in $\Omega$ and with $\int _{\Omega} f \; dx=0$ a scala …
enrico's user avatar
  • 71
6 votes
1 answer
1k views

Gradient estimate for elliptic equation

Given: 1)a bounded domain $\Omega$ in $\mathbb R^n$ of class $\mathcal{C}^{\infty}$ 2) the function $f\in L^{\infty}(\Omega)$ with $\int_{\Omega} f=0$ 3)$g=(g_i,\ldots,g_n)\in \mathcal{C}^\alpha(\O …
enrico's user avatar
  • 71