Vincenzo Vespri

Harnack's inequality for degenerate and singular parabolic equations

Preface.- 1. Introduction.- 2. Preliminaries.- 3. Degenerate and Singular Parabolic Equations.- 4. Expansion of Positivity.- 5. The Harnack Inequality for Degenerate Equations.- 6. The Harnack Inequality for Singular Equations.- 7. Homogeneous Monotone Singular Equations.- Appendix A.- Appendix B.- Appendix C.- References.- Index.

SOME RESULTS ON PARTIAL DIFFERENTIAL EQUATIONS AND ASIAN OPTIONS

We analyze partial differential equations arising in the evaluation of Asian options. The equations are strongly degenerate partial differential equations in three dimensions. We show that the solution of the no-arbitrage partial differential equation is sufficiently regular and standard numerical methods can be employed to approximate it.

On the local behaviour of solutions of a certain class of doubly nonlinear parabolic equations

Here we prove Hölder regularity for bounded weak solutions of nonlinear parabolic equations with measurable coefficients. The prototype of this class of equations isut=Div(|u|β|Du|p−2Du)p>1, β>1−p

Generation of analytic semigroups by elliptic operators with unbounded coefficents

Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate analytic semigroups of linear operators on

Analytic semigroups, degenerate elliptic operators and applications to nonlinear cauchy problems

L^2 (R^N )

Generation of analytic semigroups in theL p topology by elliptic operators inR n

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A new proof of the Hölder continuity of solutions to p-Laplace type parabolic equations

L^{2,\mu } (R^N )

Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations

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Hölder regularity in variational parabolic non-homogeneous equations

C(R^N )

Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations

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