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Vietnam Journal of Mathematics 37:2&3 (2009) 387-397  Recent Results in the Theory of Semilinear Elliptic Degenerate Differential Equations Nguyen Minh Tri Abstract.  In this paper we give a survey on recent study of semilinear elliptic degenerate differential equations. Here we will discuss the critical exponents phenomenon for boundary value problems and interior regularities of solutions of various classes of such equations. Similar problems for nonlinear elliptic equations were studied in [2, 3, 10, 12, 13, 19, 24, 25, 28, 30-32, 44]. 2000 Mathematics Subject Classification: Primary 35-02; Secondary 32V99, 33C05, 33C65, 35A08, 35B65, 35C15, 35H10, 35J70. Keywords: Elliptic degenerate equations, semilinear equations, critical exponents, regularity of solutions.

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