Nonlinear Elliptic Partial Differential Equations pp 141-178 | Cite as

# Calculus of Variations and Quasilinear Problems

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## Abstract

The nonlinear elliptic problems studied up to now were what is called *semilinear* problems. Semilinear problems are nonlinear problems in which the nonlinearity only concerns the terms that involve derivatives of order strictly less than the maximum differentiation order appearing in the operator. Such is the case for instance of the term *f*(*u*) of the first model problem, with derivatives of order 0, compared to the term − Δ*u* which contains all the derivatives of the highest order, namely here 2, involved in the problem. In a semilinear problem, the principal part of the operator remains a linear operator.

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