We study elliptic and parabolic problems governed by the singular elliptic operators L=y(alpha 1) Tr (QD(x)(2))+2y alpha(1)+alpha(2)/2q & sdot;del D-x(y)+gamma y(alpha 2)D(yy) +y alpha(1)+alpha(2)/2-1(d,del(x))+cy(alpha 2-1)D(y)-by(alpha 2-2) in the half-space R-+(N+1)={(x,y):x is an element of R-N,y>0}, under Dirichlet or oblique derivative boundary conditions. In the special case alpha 1=alpha 2=alpha the operator L takes the form L=y(alpha) Tr (AD(2))+y(alpha-1)(v,del)-by(alpha-2), where v=(d,c)is an element of RN+1, b is an element of R and A=(Q/q(t) q/gamma) is an elliptic matrix. We prove elliptic and parabolic Lp-estimates and solvability for the associated problems. In the language of semigroup theory, we prove that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space and show that it has maximal regularity.
Singular parabolic operators in the half-space with boundary degeneracy: Dirichlet and oblique derivative boundary conditions
Negro L.
Primo
2025-01-01
Abstract
We study elliptic and parabolic problems governed by the singular elliptic operators L=y(alpha 1) Tr (QD(x)(2))+2y alpha(1)+alpha(2)/2q & sdot;del D-x(y)+gamma y(alpha 2)D(yy) +y alpha(1)+alpha(2)/2-1(d,del(x))+cy(alpha 2-1)D(y)-by(alpha 2-2) in the half-space R-+(N+1)={(x,y):x is an element of R-N,y>0}, under Dirichlet or oblique derivative boundary conditions. In the special case alpha 1=alpha 2=alpha the operator L takes the form L=y(alpha) Tr (AD(2))+y(alpha-1)(v,del)-by(alpha-2), where v=(d,c)is an element of RN+1, b is an element of R and A=(Q/q(t) q/gamma) is an elliptic matrix. We prove elliptic and parabolic Lp-estimates and solvability for the associated problems. In the language of semigroup theory, we prove that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space and show that it has maximal regularity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
