2019
Том 71
№ 8

All Issues

Bonafede S.

Articles: 3
Article (English)

On Hölder continuity of solutions of doubly nonlinear parabolic equations with weight

Bonafede S., Skrypnik I. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 890–903

We prove the Hölder regularity of bounded weak solutions of doubly nonlinear degenerate parabolic equations with measurable coefficients.

Article (Russian)

Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. II

Bonafede S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1601–1609

We use energy methods to prove the existence and uniqueness of solutions of the Dirichlet problem for an elliptic nonlinear second-order equation of divergence form with a superlinear tem [i.e., g(x, u)=v(x) a(x)⋎u⋎ p−1u,p>1] in unbounded domains. Degeneracy in the ellipticity condition is allowed. Coefficients a i,j(x,r) may be discontinuous with respect to the variable r.

Article (Ukrainian)

Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. I

Bonafede S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 867-875

This paper is concerned with the existence and uniqueness of variational solutions of the strongly nonlinear equation $$ - \sum\limits_1^m {_i \frac{\partial }{{\partial x_i }}\left( {\sum\limits_1^m {_j a_{i,j} (x, u(x))\frac{{\partial u(x)}}{{\partial x_j }}} } \right) + g(x, u(x)) = f(x)} $$ with the coefficients a i,j (x, s) satisfying an eHipticity degenerate condition and hypotheses weaker than the continuity with respect to the variable s. Furthermore, we establish a condition on f under which the solution is bounded in a bounded open subset Ω of Rm.