Elliptic equations and systems with nonstandard growth conditions: Existence, uniqueness and localization properties of solutions
โ Scribed by Stanislav Antontsev; Sergei Shmarev
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 492 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0362-546X
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๐ SIMILAR VOLUMES
## Abstract We prove a removability result for nonlinear elliptic equations with__p__ (__x__)โtype nonstandard growth and estimate the growth of solutions near a nonremovable isolated singularity. To accomplish this, we employ a Harnack estimate for possibly unbounded solutions and the fact that so
We prove the existence and uniqueness of a renormalized solution to nonlinear elliptic equations with variable exponents and L 1 -data. The functional setting involves Sobolev spaces with variable exponents W 1,p(โข) (โฆ).
Let \(\Omega\) be a smooth bounded domain of \(\mathbb{R}^{n}, n \geqslant 3\), and let \(a(x)\) and \(f(x)\) be two smooth functions defined on a neighbourhood of \(\Omega\). First we study the existence of nodal solutions for the equation \(\Delta u+a(x) u=f(x)|u|^{4 /(n-2)} u\) on \(\Omega, u=0\)