On singular elliptic equations with measure sources

By Francescantonio Oliva, Francesco Petitta. 2015

85 citations recorded by the source corpus.

We prove existence of solutions for a class of singular elliptic problems with a general measure as source term whose model is \begin{eqnarray} \begin{cases} \dys -\Delta u = \frac{f(x)}{u^{\gamma}} +\mu & \text{in}\ \Omega,\\[2mm] u=0 &\text{on}\ \partial\Omega,\\[2mm] u>0 &\text{on}\ \Omega, \end{cases} \end{eqnarray} where Ω is an open bounded subset of ℝ N . Here γ > 0, f is a nonnegative function on Ω , and μ is a nonnegative bounded Radon measure on Ω .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3516b6f246d191490b5f692b8376c243a920c537

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In Applied Mathematics

1. Luigi Montoro
2. Marco Squassina
3. A. Canino
4. Berardino Sciunzi
5. Vicentiu D. Rădulescu
6. Alberto Farina
7. R. Arora
8. Patrick Winkert

In Computational Theory and Mathematics

1. Luigi Montoro
2. A. Canino
3. Marco Squassina
4. Berardino Sciunzi
5. Alberto Farina
6. Patrick Winkert
7. Lucio Damascelli

In Mathematical Physics

1. Luigi Montoro
2. Berardino Sciunzi
3. Marco Squassina
4. A. Canino

Citations in the corpus

• Nonlocal problems with singular nonlinearity (2016, methodology): “ solution is implicitly proved in the case f= 1, p= 2 and s= 1. Such a technique was already improved in [10] in the local semilinear case. In this setting it is worth mentioning the recent result in [24] where singular problems with measure data are considered. The local quasilinear case p6= 2 was ”