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A weighted \(W^{2,p}\)-a priori bound for a class of elliptic operators. (English) Zbl 1284.35157
Summary: We prove a weighted \(W^{2,p}\)-a priori bound, \(p>1\), for a class of uniformly elliptic second-order differential operators on unbounded domains. We deduce a uniqueness and existence result for the solution of the related Dirichlet problem.

MSC:
35J25 Boundary value problems for second-order elliptic equations
35B45 A priori estimates in context of PDEs
35R05 PDEs with low regular coefficients and/or low regular data
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:
[1] doi:10.1007/BF02412185 · Zbl 0156.34001 · doi:10.1007/BF02412185
[2] doi:10.1007/BF01766150 · Zbl 0674.35020 · doi:10.1007/BF01766150
[3] doi:10.1016/S0022-247X(02)00287-1 · Zbl 1055.35038 · doi:10.1016/S0022-247X(02)00287-1
[4] doi:10.1016/j.jmaa.2006.02.048 · Zbl 1152.35025 · doi:10.1016/j.jmaa.2006.02.048
[5] doi:10.1142/S0219199704001392 · Zbl 1077.35053 · doi:10.1142/S0219199704001392
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