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Applications of Interpolation theory to the regularity of some equasilinear PDEs
Irshaad Ahmed, Alberto Fiorenza, Maria Rosaria Formica +2
We present some regularity results on the gradient of the weak or entropic-renormalized solution to the homogeneous Dirichlet problem for the quasilinear equations of the form…
Extremal case of parabolic differential equations having discontinuous unbounded coefficients. Existence of fundamental solution for an initial Cauchy problem. Parametrix method
M. R. Formica, E. Ostrovsky, L. Sirota
We prove in this short report the existence of a fundamental solution (F.S.) for the Cauchy initial boundary problem on the whole space for the parabolic differential equation havi…
Fundamental solution for Cauchy initial value problem for parabolic PDEs with discontinuous unbounded first-order coefficient at the origin. Extension of the classical parametrix method
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous un…