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Dirichlet problem for divergence form elliptic equations with discontinuous coefficients

Sara Monsurrò and Maria Transirico*

Author Affiliations

Dipartimento di Matematica, Università di Salerno, via Ponte Don Melillo, Fisciano, (SA), 84084, Italy

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Boundary Value Problems 2012, 2012:67  doi:10.1186/1687-2770-2012-67

Published: 28 June 2012


We study the Dirichlet problem for linear elliptic second order partial differential equations with discontinuous coefficients in divergence form in unbounded domains. We establish an existence and uniqueness result and we prove an a priori bound in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/67/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/67/mathml/M1">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/67/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/67/mathml/M2">View MathML</a>.

MSC: 35J25, 35B45, 35R05.

elliptic equations; discontinuous coefficients; a priori bounds