We construct fundamental solutions of some partial differential equations of order higher than two and examine properties of these solutions and of some related integrals. The results will be used in our next paper concerning boundary-value problems for these equations.
We give some expansion formulas and the Kelvin principle for solutions of a class of iterated equations of elliptic type
We give some fundamental solutions of a class of iterated elliptic equations including Laplace equation and its iterates.
Si discute l'esistenza di soluzioni su insiemi aperti per equazioni differenziali iperbolico-ipoellittiche. Si dà una caratterizzazione geometrica quasi completa per aperti .
We prove a weighted estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.
Exact fundamental solutions are known for operators of various types. We indicate a general approach that gives various old and new fundamental solutions for operators with double characteristics. The solutions allow one to read off detailed behavior, such as the presence or absence of analytic hypoellipticity. Recent results for operators with multiple characteristics are also described.
In this paper we obtain all solutions which depend only on for a class of partial differential equations of higher order with singular coefficients.