Geodesic
On estimates for the solutions to the Dirichlet problem for the Laplacian in exterior domains
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VII, Tome 146 (1985), pp. 92-101 
P. Maremonti; V. A. Solonnikov. On estimates for the solutions to the Dirichlet problem for the Laplacian in exterior domains. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VII, Tome 146 (1985), pp. 92-101. http://geodesic.mathdoc.fr/item/ZNSL_1985_146_a5/
@article{ZNSL_1985_146_a5,
     author = {P. Maremonti and V. A. Solonnikov},
     title = {On estimates for the solutions to the {Dirichlet} problem for the {Laplacian} in exterior domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {92--101},
     year = {1985},
     volume = {146},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_146_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $u(x)$ be the solution of the exterior Dirichlet problem for the equation $\Delta u=f$ vanishing at the infinity. It is shown that the coercive estimate $\| D^2u\|_{Lp)}\leq c\| f\|_{L_p}$ holds for $p In the case $p\geq n/2$ this estimate is established for solutions of the exterior Dirichlet problem that do not vanish at the infinity but may tend to a certain constant or even blow up as a linear function (for $p>n$). Bibl. – 2. Пусть $u$ – решение уравнения $\Delta u=f$ с финитной функцией $f$ по внешней области $\Omega\subset\mathbf{R}^u$ и с условиями $u|_{\partial\Omega}=0$, $u\to0$ при $|x|\to\infty$. Показано, что коэрцитивная оценка $\|D^2u\|_{L_p(\Omega)}\leq c\|f\|$ справедлива лишь при $p. При $p\geq n/2$ она имеет место для решения внешней задачи Дирихле, которая не исчезает на бесконечности, а может стремиться к постоянной или даже к линейной (при $p>n$) функции. Библ. – 2 назв.