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Variable exponents 27 Variable exponent spaces 20 Sobolev embedding 14 Concentration compactness 12 Critical exponents 12 P (x)-Laplacian 8 Concentration-compactness principle 6 Free boundary problem 6 Laplace transforms 6 Singular perturbation 6 Sobolev spaces 5 Variable exponent 5 Asymptotic analysis 4 Elliptic equations 4 Free-boundary problems 4 H2 regularity 4 Inhomogeneous problem 4 Minimization 4 Optimization 4 Regularity of the free boundary 4 variable exponent spaces 4 CONCENTRATION COMPACTNESS PRINCIPLE 3 CRITICAL EXPONENT 3 ESPACIOS DE EXPONENTE VARIABLE 3 EXPONENTE CRITICO 3 Fractional Laplacian 3 INMERSIONES DE SOBOLEV 3 PRINCIPIO DE COMPACIDAD POR CONCENTRACION 3 SOBOLEV EMBEDDINGS 3 VARIABLE EXPONENT SPACES 3