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Comportamento alla frontiera per soluzioni di equazioni ellittiche e paraboliche

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Si presentano alcuni recenti risultati in teoria del potenziale per equazioni ellittiche e paraboliche.

Tali risultati riguardano problemi di esistenza di limiti non tangenziali, formule di rappresentazione, teoremi di confronto tra soluzioni positive all’interno di un dominio che si annullano su parti della frontiera.

Sono anche segnalati alcuni problemi aperti riguardanti le equazioni paraboliche.

Summary

We present a survey of some recent results in potential theory for elliptic and parabolic equations.

These results concern problems on existence of non-tangential limits, representation formulas, comparison theorems between positive solutions vanishing on parts of the boundary.

Some open problems on parabolic equations are also focused.

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  1. del Politeenico di Milano, Milano, Italia

    S. Salsa

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(Conferenza tenuta il 13 aprile 1987)

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Salsa, S. Comportamento alla frontiera per soluzioni di equazioni ellittiche e paraboliche. Seminario Mat. e. Fis. di Milano 57, 337–363 (1987). https://doi.org/10.1007/BF02925061

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