A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions

2016 ◽  
Vol 152 (3-4) ◽  
pp. 345-380 ◽  
Author(s):  
Tiziano Granucci
Keyword(s):  
Harnack Inequality ◽  
Growth Conditions ◽  
Integral Functionals ◽  
General Growth ◽  
Scalar Integral

scholarly journals Growth conditions and regularity, an optimal local boundedness result

2020 ◽  
pp. 2050029
Author(s):  
Jonas Hirsch ◽  
Mathias Schäffner
Keyword(s):  
Growth Conditions ◽  
Integral Functionals ◽  
Local Minimizers ◽  
Local Boundedness ◽  
Scalar Integral ◽  
Boundedness Result

We prove local boundedness of local minimizers of scalar integral functionals [Formula: see text], [Formula: see text] where the integrand satisfies [Formula: see text]-growth of the form [Formula: see text] under the optimal relation [Formula: see text].

scholarly journals Harnack’s inequality for doubly nonlinear equations of slow diffusion type

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Verena Bögelein ◽  
Andreas Heran ◽  
Leah Schätzler ◽  
Thomas Singer
Keyword(s):  
Vector Field ◽  
Harnack Inequality ◽  
Parabolic Equations ◽  
Full Range ◽  
Nonlinear Parabolic Equations ◽  
Growth Conditions ◽  
Diffusion Type ◽  
Slow Diffusion ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear

AbstractIn this article we prove a Harnack inequality for non-negative weak solutions to doubly nonlinear parabolic equations of the form $$\begin{aligned} \partial _t u - {{\,\mathrm{div}\,}}{\mathbf {A}}(x,t,u,Du^m) = {{\,\mathrm{div}\,}}F, \end{aligned}$$ ∂ t u - div A ( x , t , u , D u m ) = div F , where the vector field $${\mathbf {A}}$$ A fulfills p-ellipticity and growth conditions. We treat the slow diffusion case in its full range, i.e. all exponents $$m > 0$$ m > 0 and $$p>1$$ p > 1 with $$m(p-1) > 1$$ m ( p - 1 ) > 1 are included in our considerations.

scholarly journals Regularity under sharp anisotropic general growth conditions

2009 ◽  
Vol 11 (1) ◽  
pp. 67-86
Author(s):  
Giovanni Cupini ◽  
◽  
Paolo Marcellini ◽  
Elvira Mascolo
Keyword(s):  
Growth Conditions ◽  
General Growth
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